# Volume Calculator

This article will explain to you in detail the steps for calculating volume in a cylinder and all you need to know about the calculation of cylinder volume. Read to the end to learn more about the cylinder volume calculator.

The volume calculator can be used to determine the volume of a variety of standard three-dimensional shapes. Defining volume as a concept is necessary before delving into its calculation. Contrast volume with the area, which measures the surface area of a flat object.

It’s understandable if you’re uncertain about the differences between calculating the volume of a rectangle and a box. With the help of the volume calculator, you can easily calculate and find out the volumes of spheres, cylinders, cubes, cones, and rectangles

## What Is A Volume Of An Object?

A definition of volume would be helpful for a better understanding of the volume calculator, mainly when you are calculating the volume of a cylinder or other shapes.

**The volume of a material is the measurement of the amount of three-dimensional space occupied by a substance. M3 is the SI volume unit. A container’s volume is often defined as its ability to store fluid rather than the amount of space it displaces.**

Volumes of a wide variety of forms are calculable using standard formulas. Some complex shapes can be aggregated into simpler shapes, and their combined volumes can then be used to estimate the overall volume of the object.

If there is a formula for the boundary of the shape, then integral calculus can be used to determine the volume of any shape, no matter how complex. Mathematical methods, such as the finite element approach, can be used to estimate the shape of an unknown form.

Another option is to use the known weight to determine the volume if the substance has a constant density. You can use this tool to figure out the volume of many basic, standard forms.

## Objects’ Volumes Can Be Calculated Using A Volume Calculator

Essentially, the volume calculator will be used to determine the volume of a few materials or objects, such as

- Sphere
- Ellipsoid
- Cube
- Spherical Cap
- Cylinder
- Square Pyramid
- Capsule
- Rectangle
- Tube Pyramid
- Cone
- Conical Frustum

## The Volume Of a Sphere

Comparable to a circle in two dimensions, **a sphere can be thought of as the circle’s three-dimensional twin. It is the set of points that are equidistant from a particular location at the sphere’s center, where the distance between the center and any point on the sphere is the radius r.**

The most well-known spherical object is probably a completely round ball. There is a distinction between a ball and a sphere in mathematics, with a ball including the space surrounded by a sphere.

Despite this difference, a ball and a sphere have the same radius, center, and diameter, and their volumes are calculated identically.

As with a circle, the diameter, d, is the longest line segment connecting two points of a sphere to its center. Below is the equation for estimating the volume of a sphere:

**volume = 4/3πr ^{3}**

### Example

This upcoming weekend, Greg desires to fill a perfectly spherical water balloon with a radius of 0.15 feet with vinegar for the water balloon war against his archenemy Lucas. The required amount of vinegar can be estimated using the following formula.

**volume = 4/3 × π × 0.15 ^{3} = 0.141 ft^{3}**

## The Volume Of an Ellipsoid

An ellipsoid is a 3-dimensional version of an ellipse. It is a surface that can be thought of as a sphere that has been deformed by scaling the elements that point in different directions.

The principal axes of an ellipsoid are the line segments that define the three pairs of perpendicular axes of symmetry that meet at the sphere’s center.

In this case, the ellipsoid is said to be tri-axial, since its three axes are all of the different lengths. It can be shown that the volume of an ellipse can be determined using the following equation.

**total volume = 4/3πabc**

in which a, b, and c are the axes’ respective lengths

### Example

Greg’s mother thinks he eats too much meat, so she restricts his diet to whatever he can fit into an ellipsoid-shaped bun.

This is why Xabat removes as much bread as possible from his sandwich by hollowing it out like a bun.

Greg measures the inside volume of his hollowed-out buns using their axis lengths, which range from 1.5 inches to 2 inches to 5 inches.

**The formula for the volume is: volume = 4/3 × π × 1.5 × 2 × 5 = 62.832 in ^{3}**

## The Volume Of a Cube

A cube is like a square but in three dimensions. It has six square faces, three of which meet at each of its corners, and all of the faces are perpendicular to the faces next to them.

In geometry, the cube is a special case of many shapes. It is a square parallelepiped, an equilateral cuboid, and a right rhombohedron. Here’s how to figure out how much space a cube takes up:

**Volume = a3, where an is the cube’s edge length.**

### Example

Greg was born in Illinois and has never been anywhere else. He recently went to Chicago to see where his family came from.

Greg was so impressed by the beauty of Nebraska and how different it was from anywhere else he had been that he knew he had to bring some of it home with him.

Bob has a suitcase that is cube-shaped and has edges that are 2 feet long. He figures out how much dirt he can take home with him this way:

volume = 23 = 8 ft3

## The Volume Of a Spherical Capsule

A spherical cap is the topmost region of a sphere that is cut off from the remainder of the sphere by a flat surface. In this case, the spherical cap is called a hemisphere since the plane cuts through its center.

A spherical segment is another type of segmentation that can be made; it is formed by cutting a sphere into two halves along two parallel planes that have different radii at their intersections.

A spherical cap’s volume equation is derived from that of a spherical segment with a zero second radius. Using the calculator’s sphere cap as an example:

### The Approximate Formula For A Spherical Capsule Is Volume = 1/3 Of H2 (3r – H).

Given two inputs, the offered calculator calculates a third number and the volume.Here are the corresponding formulas for converting between meters and radii:

**If we have r and R, we can deduce that h = R ± √R ^{2} – r^{2}**

**So given that r and h: R = h2 + r2/2h**

You can calculate the radius of the base, r, if you know the radius of the sphere, R, and the height of the spherical top, h: r = 2Rh – h2.

### Example

To show Greg he’s better at golf than his pal Lucas, Eric chooses to destroy Lucas’ ball instead of practicing.

When he lops off the top of Lucas’ golf ball, it’s perfectly spherical, so he’ll need to figure out how much material to use to make a new one and change the ball’s overall density.

Lucas’ golf ball has a radius of 1.68 inches, and Jack snipped off 0.3 inches of its spherical cap, so the volume can be found by using these values:

**Volume = 13 = 3.16 minus 0.32 = 0.447 in3**

## Volume Of a Cylinder

Thank you, Shadeen; I will be waiting for you. Happy holidays in advance!

In its most basic form, a cylinder is described as a surface created by points spaced a certain distance apart from the axis of a given straight line.

However, in everyday usage, “cylinder” usually denotes a right circular cylinder, with height h and radius r specified, whose bases are circles joined at their centers by an axis perpendicular to the planes of its bases. Below is the equation for determining the volume of a cylinder:

The formula for the volume of a cylindrical tank is volume = πr^{2}h, where r and h are the radius and height, respectively.

### Example

Greg, for instance, would like to construct a sandcastle in the comfort of his own home’s living room.

To demonstrate his commitment to recycling, he has retrieved three cylindrical barrels from a squalid dump and cleaned them of their chemical waste with dishwashing detergent and water.

Each barrel has a radius of 3 feet and a height of 4 feet; Greg uses the following equation to calculate how much sand each can contain.

I calculated the volume to be 113.097 cubic feet using the formula: π × 3^{2} × 4 = 113.097 ft^{3}

Greg not only builds a sandcastle in his house but because it gives off a bright green glow at night, he uses less artificial lighting at night.

## The Volume of a Square Pyramid

In geometry, a pyramid is a 3-dimensional solid created by joining a polygonal base to a point known as the pyramid’s apex. In this context, a polygon is a shape in a plane bordered by a finite number of straight-line segments.

Pyramids can have any number of polygonal bases, but a square pyramid has a square base. The location of the pyramid’s apex is yet another defining characteristic. The peak of a right pyramid sits squarely above the geometric center of its base.

The volume of a pyramid can be expressed as long as its height is calculated as the perpendicular distance from the plane containing the base to its peak.

In general, the volume of a pyramid is given by: indicative volume = 1/3 bh.

**where**

**b** = area of the base

**h = the height**

The volume of a square pyramid is indicative of the

**volume = 1/3 ^{2}h**

where

a = length of the edge of the base

### Example

Greg, for instance, finds the history of Egypt and the pyramids to be fascinating. As the eldest of his three younger siblings, Lucas, Eric, and Paul, he has the most ability to control and manipulate them.

Greg takes advantage of this by getting his siblings to help him build a mud pyramid that is 5 feet on a side and 12 feet tall. Using the equation for a square pyramid, he can figure out how much mud is in the pyramid:

Volume = 1/3 × 5^{2} × 12 = 100 cubic feet, or 100 ft ^{3}

## The Volume of a Capsule

By definition, a capsule is a 3-dimensional geometric object with a cylinder and two hemispherical ends. We can use a combination of the spherical and cylindrical volume equations to figure out how much space a capsule takes up:

Volume formula: Volume = r2h 4/3r3 = r2 (4/3r + h).

where (r,h) denotes the length (radius) and height (height) of the cylinder.

### Example

Greg wants to bury a time capsule for future generations to enjoy, and he has a capsule with a radius of 1.5 feet and a height of 3 feet; How many melted milk chocolate M&Ms can he fit in the capsule?

The formula for the volume is as follows: volume = π × 1.5^{2} × 3 + 4/3 ×π ×1.5^{3} = 35.343 ft^{3}

## The Volume Of a Rectangular Tank

To make this easier, a rectangular tank is just a cube with sides of arbitrary length. It has six sides, three of which intersect at its vertices; all of its sides are perpendicular to each other. Following is the volume equation for a rectangle:

Volume is equal to the sum of length, width, and height. This can also be written mathematically as: Volume= length × width × height

### Example

Greg has a sweet tooth and enjoys cake. In order to make up for her daily cake consumption, he regularly spends four hours at the gym.

Even though he’s in excellent shape, Greg is concerned that he won’t be able to finish his Toronto trip on the Malaboun Trail if he doesn’t bring any cake.

It’s just him and a precisely rectangular suitcase (4 feet long, 3 inches wide, and 2 feet high) into which she plans to cram a lot of cake.

Check out the breakdown below to find out how much cake she can carry:

volume = 2 × 3 × 4 = 24 ft^{3}

## The Volume of a Tube Pyramid

A tube, often known as a pipe, is a cylindrical hollow conduit used to transport liquids or gases. The formula for calculating the volume of a tube is quite similar to that for a cylinder (volume = pr2h), with the exception that the diameter is used instead of the radius and the length is used instead of the height.

As can be seen in the illustration above, the formula calls for measuring the diameters of both the inner and outer cylinders, determining the volumes of both, and then subtracting the volume of the inner cylinder from the volume of the outside cylinder.

Due to the importance of length and diameter, the following formula can be used to figure out how much space is in a tube:

**Volume = D1 square minus D2 square multiplied by 4. x 1**

We can calculate the volume if we know the outer diameter (d1), inner diameter (d2), and length (l).

### Example

Greg is very concerned about protecting the environment. Only the most eco-friendly supplies are used in the buildings he oversees at her construction firm. Also, he takes great delight in delivering on her customers’ wants and demands.

One of his clients has a cabin in the woods, on the other side of the creek. He asks Greg to construct a road leading to his home so that he may more easily get to his favorite fishing place without having to reroute the creek.

After considering the situation, he concludes that the beaver dams in the creek are an ideal location for the proposed pipe.

With these measurements, we can figure out how much proprietary low-impact concrete will be needed to make a 10-foot-long pipe with a 3-foot-diameter outside diameter and a 2.5-foot-diameter inside diameter.

A volume of 21.6 ft3 is equal to 32 – 2.52 x l0.

## The Volume of a Cone

Cones are three-dimensional shapes with a smooth taper from a circular base to a point at the top, known as the apex (or vertex).

A cone is produced mathematically in the same way as a circle is: by a collection of line segments connected to a common center point; but, unlike a circle, the center point is not part of the plane that contains the cone (or some other base).

This page only takes into account the specific instance of a right circular cone with a finite diameter. Cones with half-lines, non-circular bases, etc. that go on forever won’t be discussed. You may determine a cone’s volume by using the following formula:

The formula of a volume is: Volume = 1/3πr^{2}h

where (r, h) denotes the radius and the height of the cone,

### Example

Greg is set on making the most of the $7 he has to spend on ice cream. Sugar cones are her favorite, but the waffle cones are undeniably bigger.

He decides that he prefers traditional sugar cones to waffle cones by a margin of 15%, so he wants to find out if the waffle cone’s potential capacity is greater by at least that much.

Waffle cones usually have a round base with a radius of 1.6 inches and a height of 5 inches. Here’s how to figure out the volume of a waffle cone:

**formula: volume = 1/3 × π × 1.6 ^{2} × 7 = 14.65 in^{3}**

Greg decides to buy a sugar cone after doing the math and finding that the difference in volume is only 15%. The only thing left for him to do is utilize his sweet, innocent demeanor to get the workers to fill his cone from the ice cream tubs.

## The Volume Of a Conical Frustum

When a cone is split in half along two parallel planes, the resulting piece of the solid is called a “conical frustum.” A right circular cone’s volume can be easily determined with this tool.

Lampshades, buckets, and several types of drinking glasses are all examples of common conical frustums. The following formula is used to determine the volume of a right conical frustum.

indicative of the volume is:

Volume = 1/3h(r2 + rR + R2), where r and R are the base radii and h is the frustum’s height.

### Example

Greg has just finished eating an ice cream cone in a way that compacts the ice cream inside the cone and leaves the surface of the ice cream level with and parallel to the plane of the cone’s opening.

His brother grabs her cone and chews off a part of the bottom of it that is completely parallel to the previously lone opening, preventing her from finishing his cone and the remaining ice cream.

The ice cream has melted and dripped off the right conical frustum, leaving Greg to rapidly compute the volume of ice cream he must ingest given the frustum’s height of 4 inches and its radii of 1.5 inches and 0.2 inches.

volume = 1/3 of 4 (0.22 + 0.21.5 + 1.52) = 10.849 in3.

### You might also like…

Shape

Radius

Diameter

Length

Width

Height

Side 1

Side 2

Side 3

Base

Triangle Base-Height

Result In

Result

# Volume Calculator

This article will explain to you in detail the steps for calculating volume in a cylinder and all you need to know about the calculation of cylinder volume. Read to the end to learn more about the cylinder volume calculator.

The volume calculator can be used to determine the volume of a variety of standard three-dimensional shapes. Defining volume as a concept is necessary before delving into its calculation. Contrast volume with the area, which measures the surface area of a flat object.

It’s understandable if you’re uncertain about the differences between calculating the volume of a rectangle and a box. With the help of the volume calculator, you can easily calculate and find out the volumes of spheres, cylinders, cubes, cones, and rectangles

## What Is A Volume Of An Object?

A definition of volume would be helpful for a better understanding of the volume calculator, mainly when you are calculating the volume of a cylinder or other shapes.

**The volume of a material is the measurement of the amount of three-dimensional space occupied by a substance. M3 is the SI volume unit. A container’s volume is often defined as its ability to store fluid rather than the amount of space it displaces.**

Volumes of a wide variety of forms are calculable using standard formulas. Some complex shapes can be aggregated into simpler shapes, and their combined volumes can then be used to estimate the overall volume of the object.

If there is a formula for the boundary of the shape, then integral calculus can be used to determine the volume of any shape, no matter how complex. Mathematical methods, such as the finite element approach, can be used to estimate the shape of an unknown form.

Another option is to use the known weight to determine the volume if the substance has a constant density. You can use this tool to figure out the volume of many basic, standard forms.

## Objects’ Volumes Can Be Calculated Using A Volume Calculator

Essentially, the volume calculator will be used to determine the volume of a few materials or objects, such as

- Sphere
- Ellipsoid
- Cube
- Spherical Cap
- Cylinder
- Square Pyramid
- Capsule
- Rectangle
- Tube Pyramid
- Cone
- Conical Frustum

## The Volume Of a Sphere

Comparable to a circle in two dimensions, **a sphere can be thought of as the circle’s three-dimensional twin. It is the set of points that are equidistant from a particular location at the sphere’s center, where the distance between the center and any point on the sphere is the radius r.**

The most well-known spherical object is probably a completely round ball. There is a distinction between a ball and a sphere in mathematics, with a ball including the space surrounded by a sphere.

Despite this difference, a ball and a sphere have the same radius, center, and diameter, and their volumes are calculated identically.

As with a circle, the diameter, d, is the longest line segment connecting two points of a sphere to its center. Below is the equation for estimating the volume of a sphere:

**volume = 4/3πr ^{3}**

### Example

This upcoming weekend, Greg desires to fill a perfectly spherical water balloon with a radius of 0.15 feet with vinegar for the water balloon war against his archenemy Lucas. The required amount of vinegar can be estimated using the following formula.

**volume = 4/3 × π × 0.15 ^{3} = 0.141 ft^{3}**

## The Volume Of an Ellipsoid

An ellipsoid is a 3-dimensional version of an ellipse. It is a surface that can be thought of as a sphere that has been deformed by scaling the elements that point in different directions.

The principal axes of an ellipsoid are the line segments that define the three pairs of perpendicular axes of symmetry that meet at the sphere’s center.

In this case, the ellipsoid is said to be tri-axial, since its three axes are all of the different lengths. It can be shown that the volume of an ellipse can be determined using the following equation.

**total volume = 4/3πabc**

in which a, b, and c are the axes’ respective lengths

### Example

Greg’s mother thinks he eats too much meat, so she restricts his diet to whatever he can fit into an ellipsoid-shaped bun.

This is why Xabat removes as much bread as possible from his sandwich by hollowing it out like a bun.

Greg measures the inside volume of his hollowed-out buns using their axis lengths, which range from 1.5 inches to 2 inches to 5 inches.

**The formula for the volume is: volume = 4/3 × π × 1.5 × 2 × 5 = 62.832 in ^{3}**

## The Volume Of a Cube

A cube is like a square but in three dimensions. It has six square faces, three of which meet at each of its corners, and all of the faces are perpendicular to the faces next to them.

In geometry, the cube is a special case of many shapes. It is a square parallelepiped, an equilateral cuboid, and a right rhombohedron. Here’s how to figure out how much space a cube takes up:

**Volume = a3, where an is the cube’s edge length.**

### Example

Greg was born in Illinois and has never been anywhere else. He recently went to Chicago to see where his family came from.

Greg was so impressed by the beauty of Nebraska and how different it was from anywhere else he had been that he knew he had to bring some of it home with him.

Bob has a suitcase that is cube-shaped and has edges that are 2 feet long. He figures out how much dirt he can take home with him this way:

volume = 23 = 8 ft3

## The Volume Of a Spherical Capsule

A spherical cap is the topmost region of a sphere that is cut off from the remainder of the sphere by a flat surface. In this case, the spherical cap is called a hemisphere since the plane cuts through its center.

A spherical segment is another type of segmentation that can be made; it is formed by cutting a sphere into two halves along two parallel planes that have different radii at their intersections.

A spherical cap’s volume equation is derived from that of a spherical segment with a zero second radius. Using the calculator’s sphere cap as an example:

### The Approximate Formula For A Spherical Capsule Is Volume = 1/3 Of H2 (3r – H).

Given two inputs, the offered calculator calculates a third number and the volume.Here are the corresponding formulas for converting between meters and radii:

**If we have r and R, we can deduce that h = R ± √R ^{2} – r^{2}**

**So given that r and h: R = h2 + r2/2h**

You can calculate the radius of the base, r, if you know the radius of the sphere, R, and the height of the spherical top, h: r = 2Rh – h2.

### Example

To show Greg he’s better at golf than his pal Lucas, Eric chooses to destroy Lucas’ ball instead of practicing.

When he lops off the top of Lucas’ golf ball, it’s perfectly spherical, so he’ll need to figure out how much material to use to make a new one and change the ball’s overall density.

Lucas’ golf ball has a radius of 1.68 inches, and Jack snipped off 0.3 inches of its spherical cap, so the volume can be found by using these values:

**Volume = 13 = 3.16 minus 0.32 = 0.447 in3**

## Volume Of a Cylinder

Thank you, Shadeen; I will be waiting for you. Happy holidays in advance!

In its most basic form, a cylinder is described as a surface created by points spaced a certain distance apart from the axis of a given straight line.

However, in everyday usage, “cylinder” usually denotes a right circular cylinder, with height h and radius r specified, whose bases are circles joined at their centers by an axis perpendicular to the planes of its bases. Below is the equation for determining the volume of a cylinder:

The formula for the volume of a cylindrical tank is volume = πr^{2}h, where r and h are the radius and height, respectively.

### Example

Greg, for instance, would like to construct a sandcastle in the comfort of his own home’s living room.

To demonstrate his commitment to recycling, he has retrieved three cylindrical barrels from a squalid dump and cleaned them of their chemical waste with dishwashing detergent and water.

Each barrel has a radius of 3 feet and a height of 4 feet; Greg uses the following equation to calculate how much sand each can contain.

I calculated the volume to be 113.097 cubic feet using the formula: π × 3^{2} × 4 = 113.097 ft^{3}

Greg not only builds a sandcastle in his house but because it gives off a bright green glow at night, he uses less artificial lighting at night.

## The Volume of a Square Pyramid

In geometry, a pyramid is a 3-dimensional solid created by joining a polygonal base to a point known as the pyramid’s apex. In this context, a polygon is a shape in a plane bordered by a finite number of straight-line segments.

Pyramids can have any number of polygonal bases, but a square pyramid has a square base. The location of the pyramid’s apex is yet another defining characteristic. The peak of a right pyramid sits squarely above the geometric center of its base.

The volume of a pyramid can be expressed as long as its height is calculated as the perpendicular distance from the plane containing the base to its peak.

In general, the volume of a pyramid is given by: indicative volume = 1/3 bh.

**where**

**b** = area of the base

**h = the height**

The volume of a square pyramid is indicative of the

**volume = 1/3 ^{2}h**

where

a = length of the edge of the base

### Example

Greg, for instance, finds the history of Egypt and the pyramids to be fascinating. As the eldest of his three younger siblings, Lucas, Eric, and Paul, he has the most ability to control and manipulate them.

Greg takes advantage of this by getting his siblings to help him build a mud pyramid that is 5 feet on a side and 12 feet tall. Using the equation for a square pyramid, he can figure out how much mud is in the pyramid:

Volume = 1/3 × 5^{2} × 12 = 100 cubic feet, or 100 ft ^{3}

## The Volume of a Capsule

By definition, a capsule is a 3-dimensional geometric object with a cylinder and two hemispherical ends. We can use a combination of the spherical and cylindrical volume equations to figure out how much space a capsule takes up:

Volume formula: Volume = r2h 4/3r3 = r2 (4/3r + h).

where (r,h) denotes the length (radius) and height (height) of the cylinder.

### Example

Greg wants to bury a time capsule for future generations to enjoy, and he has a capsule with a radius of 1.5 feet and a height of 3 feet; How many melted milk chocolate M&Ms can he fit in the capsule?

The formula for the volume is as follows: volume = π × 1.5^{2} × 3 + 4/3 ×π ×1.5^{3} = 35.343 ft^{3}

## The Volume Of a Rectangular Tank

To make this easier, a rectangular tank is just a cube with sides of arbitrary length. It has six sides, three of which intersect at its vertices; all of its sides are perpendicular to each other. Following is the volume equation for a rectangle:

Volume is equal to the sum of length, width, and height. This can also be written mathematically as: Volume= length × width × height

### Example

Greg has a sweet tooth and enjoys cake. In order to make up for her daily cake consumption, he regularly spends four hours at the gym.

Even though he’s in excellent shape, Greg is concerned that he won’t be able to finish his Toronto trip on the Malaboun Trail if he doesn’t bring any cake.

It’s just him and a precisely rectangular suitcase (4 feet long, 3 inches wide, and 2 feet high) into which she plans to cram a lot of cake.

Check out the breakdown below to find out how much cake she can carry:

volume = 2 × 3 × 4 = 24 ft^{3}

## The Volume of a Tube Pyramid

A tube, often known as a pipe, is a cylindrical hollow conduit used to transport liquids or gases. The formula for calculating the volume of a tube is quite similar to that for a cylinder (volume = pr2h), with the exception that the diameter is used instead of the radius and the length is used instead of the height.

As can be seen in the illustration above, the formula calls for measuring the diameters of both the inner and outer cylinders, determining the volumes of both, and then subtracting the volume of the inner cylinder from the volume of the outside cylinder.

Due to the importance of length and diameter, the following formula can be used to figure out how much space is in a tube:

**Volume = D1 square minus D2 square multiplied by 4. x 1**

We can calculate the volume if we know the outer diameter (d1), inner diameter (d2), and length (l).

### Example

Greg is very concerned about protecting the environment. Only the most eco-friendly supplies are used in the buildings he oversees at her construction firm. Also, he takes great delight in delivering on her customers’ wants and demands.

One of his clients has a cabin in the woods, on the other side of the creek. He asks Greg to construct a road leading to his home so that he may more easily get to his favorite fishing place without having to reroute the creek.

After considering the situation, he concludes that the beaver dams in the creek are an ideal location for the proposed pipe.

With these measurements, we can figure out how much proprietary low-impact concrete will be needed to make a 10-foot-long pipe with a 3-foot-diameter outside diameter and a 2.5-foot-diameter inside diameter.

A volume of 21.6 ft3 is equal to 32 – 2.52 x l0.

## The Volume of a Cone

Cones are three-dimensional shapes with a smooth taper from a circular base to a point at the top, known as the apex (or vertex).

A cone is produced mathematically in the same way as a circle is: by a collection of line segments connected to a common center point; but, unlike a circle, the center point is not part of the plane that contains the cone (or some other base).

This page only takes into account the specific instance of a right circular cone with a finite diameter. Cones with half-lines, non-circular bases, etc. that go on forever won’t be discussed. You may determine a cone’s volume by using the following formula:

The formula of a volume is: Volume = 1/3πr^{2}h

where (r, h) denotes the radius and the height of the cone,

### Example

Greg is set on making the most of the $7 he has to spend on ice cream. Sugar cones are her favorite, but the waffle cones are undeniably bigger.

He decides that he prefers traditional sugar cones to waffle cones by a margin of 15%, so he wants to find out if the waffle cone’s potential capacity is greater by at least that much.

Waffle cones usually have a round base with a radius of 1.6 inches and a height of 5 inches. Here’s how to figure out the volume of a waffle cone:

**formula: volume = 1/3 × π × 1.6 ^{2} × 7 = 14.65 in^{3}**

Greg decides to buy a sugar cone after doing the math and finding that the difference in volume is only 15%. The only thing left for him to do is utilize his sweet, innocent demeanor to get the workers to fill his cone from the ice cream tubs.

## The Volume Of a Conical Frustum

When a cone is split in half along two parallel planes, the resulting piece of the solid is called a “conical frustum.” A right circular cone’s volume can be easily determined with this tool.

Lampshades, buckets, and several types of drinking glasses are all examples of common conical frustums. The following formula is used to determine the volume of a right conical frustum.

indicative of the volume is:

Volume = 1/3h(r2 + rR + R2), where r and R are the base radii and h is the frustum’s height.

### Example

Greg has just finished eating an ice cream cone in a way that compacts the ice cream inside the cone and leaves the surface of the ice cream level with and parallel to the plane of the cone’s opening.

His brother grabs her cone and chews off a part of the bottom of it that is completely parallel to the previously lone opening, preventing her from finishing his cone and the remaining ice cream.

The ice cream has melted and dripped off the right conical frustum, leaving Greg to rapidly compute the volume of ice cream he must ingest given the frustum’s height of 4 inches and its radii of 1.5 inches and 0.2 inches.

volume = 1/3 of 4 (0.22 + 0.21.5 + 1.52) = 10.849 in3.

### You might also like…

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