# FINDING THE VOLUME OF A SPHERE

## About "Finding the volume of a sphere"

Finding the volume of a sphere :

We can find the volume of a sphere using the formula of volume of a cylinder.

When we model the volume of a sphere, we will be getting the following result.

Volume of cone  =  2/3 · Volume of cylinder

Substitute the formula for volume of cylinder.

Volume of the cone  =  2/3 · r²h

A sphere always has a height which is equal to twice the radius.

So, substitute 2r for h.

Volume of sphere  =  2/3 · r²(2r)

Simplify.

Volume of sphere  =  4/3 · r³

## Finding the volume of a sphere - Examples

Example 1 :

Find the volume of the sphere given below. Round your answer to the nearest tenth if necessary. Use the approximate of value of  , that is 3.14. Solution :

Step 1 :

Write the formula to find volume of a sphere.

V  =  4/3 · r³

Step 2 :

Substitute the given measures.

≈  4/3 · 3.14 · 2.2³

Simplify.

≈  4/3 · 3.14 · 10.648

≈  44.6

Hence, the volume of the given sphere is about 44.6 cubic cm.

Example 2 :

Find the volume of the sphere given below. Round your answer to the nearest tenth if necessary. Use the approximate of value of  , that is 3.14. Solution :

Step 1 :

Write the formula to find volume of a sphere.

V  =  4/3 · r³ ----- (1)

Step 2 :

To find the volume, we need the radius of the sphere. But, the diameter is given, that is  42 cm. So, find the radius.

r  =  diameter / 2

r  =  42/2

r  =  21

Step 3 :

Plug ∏ ≈  3.14 and r = 21 in (1).

≈  4/3 · 3.14 · 21³

Simplify.

≈  4/3 · 3.14 · 9261

≈  38,772.7

Hence, the volume of the given sphere is about 38,772.7 cubic cm.

Example 3 :

Find the volume of the sphere given below. Round your answer to the nearest tenth if necessary. Use the approximate of value of  , that is 3.14. Solution :

Step 1 :

Write the formula to find volume of a sphere.

V  =  4/3 · r³ ----- (1)

Step 2 :

To find the volume, we need the radius of the sphere. But, the height is given, that is  12 cm.

We know that the height of a sphere equals twice the radius.

That is,

h  =  2r

Plug h = 12.

12  =  2r

Divide both sides by 2.

12/2  =  2r/2

6  =  r

Step 3 :

Plug ∏ ≈  3.14 and r = 6 in (1).

≈  4/3 · 3.14 · 6³

Simplify.

≈  4/3 · 3.14 · 216

≈  904.3

Hence, the volume of the given sphere is about 904.3 cubic cm. After having gone through the stuff given above, we hope that the students would have understood "Finding the volume of a sphere".