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# Volume of Sphere

Think of a soccer ball, think of a globe: these are round three-dimensional objects. The shape of such objects is referred to as a sphere. In this article, we will learn how to find the volume of a sphere.

## Volume of a Sphere Meaning

To visualize a sphere, consider all possible congruent circles in space that have the same point for their center. Taken together, these circles form a sphere. All points on the surface of the sphere are an equal distance from its center. This distance is the radius of the sphere.

In space, a sphere is the locus of all points that are at a given distance from a given point – its center.

The total space occupied by a sphere is referred to as the volume of the sphere.

## The Volume of a Sphere Formula

The formula to calculate the volume V of a sphere with radius r is

Why do we use this formula to compute the volume of a sphere? You can relate finding the formula for the volume of a sphere to the volume of a right pyramid and the surface area of the sphere.

Suppose the space inside a sphere is separated into infinitely many near-pyramids, all with vertices located at the center of the sphere as shown below:

The sphere as a combination of infinite near-pyramids, California Geometry

The height of these pyramids is equal to the radius r of the sphere. The sum of the areas of all the pyramid bases equals the surface area of the sphere.Each pyramid has a volume of , where B is the area of the pyramid's base and h is its height. Then the volume of the sphere is equal to the sum of the volumes of all of the small pyramids.

### Volume of a Sphere with Diameter

Suppose that instead of the radius, you are given the diameter of the sphere. Since the diameter is twice the radius, we can simply substitute the value in the above formula. This would lead to:

## Volume of a Sphere Calculations with examples

Let us take a look at some calculations related to the volume of spheres.

### Volume of Sphere Examples

Find the volume of a sphere of radius 4.

#### Solution

A great circle is when a plane intersects a sphere so that it contains the center of the sphere. In effect, a great circle is a circle contained within the sphere whose radius is equal to the radius of the sphere. A great circle separates a sphere into two congruent halves, each called a hemisphere.

Find the volume of a sphere whose great circle has an area of 154 unit2.

#### Solution

Area of the great circle

The volume of a sphere is . Find the radius of the sphere.

#### Solution

The volume of a sphere is . Find the diameter of the sphere.

#### Solution

Find the volume of a sphere with diameter 2 units.

## Volume of Spheres - Key takeaways

• In space, a sphere is the locus of all points that are at a given distance from a given point called its center.
• The volume, V of a sphere with radius, r is given by the formula:
• The volume, V of a sphere with diameter, d is given by the formula:

The volume, V of a sphere with radius, r is given by the formula: V=(4/3)πr³

The volume, V of a sphere with radius, r is given by the formula: V=(4/3)πr³

The volume, V of a sphere with radius, r is given by the formula: V=(4/3)πr³

The volume, V of a sphere with radius, d is given by the formula: V=(1/6)πd³

## Final Volume of Sphere Quiz

Question

What is a sphere?

In space, a sphere is the locus of all points that are at a given distance from a given point called its center.

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Question

What is a great circle?

When a plane intersects a sphere so that it contains the center of the sphere, the intersection is called a great circle.

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Question

Find the volume of a sphere whose great circle has an area of 154.

1437.33

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Question

Find the volume of a sphere whose great circle has an area of 22.

543.26

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Question

A sphere has a volume of 543.26. Find its radius.

2.65

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Question

Find the volume of a sphere of radius 1

4.19

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Question

Find the volume of a sphere of radius 4

268.19

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Question

Find the volume of a sphere of radius 14.

11498.67

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Question

A sphere has a volume of 11498.67. Find its radius.

14

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Question

A sphere has a volume of 268.19. Find its radius.

4

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Question

A sphere has a volume of 14.14. Find its radius.

1.5

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Question

A sphere has a volume of 212.26. Find its radius.

3.7

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Question

Find the volume of a sphere of radius 6.

905.14

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