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Volume of a Sphere

A sphere is the locus of points. The points have equidistant from the center. It is symmetrical figure. It has no corners. In this section, we will learn the volume formula, and also learn how to find the volume of a sphere.

Definition

A sphere is a round shape solid object in three-dimensional space. It can be defined as the set of points that are all at the same distance from a given point (center). The perfect example of the sphere is the globe and ball. The following figure shows a sphere shape whose radius is r, and the diameter is d.

Volume of a Sphere

There is a slight difference between a sphere, and a circle is that a circle is a two-dimensional shape while the sphere is a three-dimensional shape.

Volume of Sphere Formula

When radius (r) is Given:

Volume of a Sphere

Where:

V: is the volume of the sphere

π:is a constant whose value is 3.14 or 22/7

r: is the radius of the sphere

When diameter (d) is Given:

Volume of a Sphere

Where:

V: is the volume of the sphere

π:is a constant whose value is 3.14 or 22/7

d: is the diameter of the sphere

When Circumference (C) is Given:

Volume of a Sphere

Where:

V: is the volume of the sphere

C: is the circumference of the sphere

π:is a constant whose value is 3.14 or 22/7

r: is the radius of the sphere

When Surface Area (A) is Given:

Volume of a Sphere

Where:

V: is the volume of the sphere

A: is the surface area of the sphere

π:is a constant whose value is 3.14 or 22/7

Let's see some examples based on the above formulas.

When the radius is given in the question:

Example 1: Find the volume of a sphere whose radius is 7 inches. Take π=3.14.

Solution:

Given, radius (r) = 7 inches

π=3.14

volume (V) =?

Volume of a Sphere

According to the formula:

Volume of a Sphere

Putting the value of r in the above formula, we get:

Volume of a Sphere

Hence, the volume of the sphere is 1436.02 inches3.

Example 2: Find the volume of a sphere whose radius is 12 cm. Take Volume of a Sphere.

Solution:

Given, radius (r) = 12 cm

Volume of a Sphere

volume (V) =?

Volume of a Sphere

According to the formula:

Volume of a Sphere

Putting the value of r in the above formula, we get:

Volume of a Sphere

Hence, the volume of the sphere is 7241.14 cm3.

When the diameter is given in the question:

Example 3: The diameter of a ball is 18 cm. Find the volume of the ball. Take Volume of a Sphere.

Solution:

Given, diameter (d) = 18 cm

Volume of a Sphere

volume (V) =?

Volume of a Sphere

According to the formula:

Volume of a Sphere

Putting the value of d in the above formula, we get:

Volume of a Sphere

Hence, the volume of the ball is 3054.85 cm3.

Example 4: The diameter of a globe is 6 feet. Find the volume of the globe.

Solution:

Given, diameter (d) = 6 ft

π=3.14

volume (V) =?

Volume of a Sphere

According to the formula:

Volume of a Sphere

Putting the value of d in the above formula, we get:

Volume of a Sphere

Hence, the volume of the globe is 113.04 ft3.

When circumference is given in the question:

Example 5: The circumference of a ball is 31.4 cm. Find the volume of the ball.

Solution:

Given, circumference (C) = 31.4 ft

π=3.14

volume (V) =?

Volume of a Sphere

According to the formula:

Volume of a Sphere

In the question, radius (r) is not given, but it is required. So, first, we will find the radius with the help of circumference.

We know that:

Circumference (C)= 2πr

Since,

Volume of a Sphere

Putting the value of C in the above formula, we get:

Volume of a Sphere

Now, we will put the value of circumference and radius in the volume formula.

Volume of a Sphere

Hence, the volume of the ball is 65.73 cm3.

When the surface area is given in the question:

Example 6: If the surface area of the sphere is 172 cm2, find the volume of the sphere.

Solution:

Given, surface area (A) = 172 cm2

π=3.14

volume (V) =?

According to the formula:

Volume of a Sphere

Putting the values in the above formula, we get:

Volume of a Sphere

Hence, the volume of the sphere is 212.4 cm3.

Example 7: The surface area of a football is 96 cm2. Find the volume of football.

Solution:

Given, surface area (A) = 96 cm2

π=3.14

volume (V) =?

According to the formula:

Volume of a Sphere

Putting the values in the above formula, we get:

Volume of a Sphere

Hence, the volume of football is 88.56 cm3.

Example 8: Find the volume of the figure given below.

Volume of a Sphere

Solution:

Given, radius (r) = 5 inches

π=3.14

volume (V) =?

According to the formula:

Volume of a Sphere

Putting the value of r in the above formula, we get:

Volume of a Sphere

Hence, the volume of the given sphere is 523.33 inches3.






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