# FINDING THE VOLUME OF A CONE

## About "Finding the volume of a cone"

Finding the volume of a cone :

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

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

Volume of cone  =  1/3 · Volume of cylinder

Substitute the formula for volume of cylinder.

Volume of the cone  =  1/3 · r²h cu. units

## Finding the volume of a cone - Examples

Example 1 :

Find the volume of the cone 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 cone.

V  =  1/3 · r²h

Step 2 :

Substitute the given measures.

≈  1/3 · 3.14 · 2² · 8

Simplify.

≈  1/3 · 3.14 · 4 · 8

≈  33.5

Hence, the volume of the given cone is about 33.5 cubic inches.

Example 2 :

Find the volume of the cone 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 cone.

V  =  1/3 · r²h ----- (1)

Step 2 :

To find the volume, we need the radius of the cone. But, the diameter is given, that is 8 ft. So, find the radius.

r  =  diameter / 2

r  =  8/2

r  =  4

Step 3 :

Plug ∏ ≈  3.14, r = 4 and h = 9 in (1).

≈  1/3 · 3.14 · 4² · 9

Simplify.

≈  1/3 · 3.14 · 16 · 9

≈  150.7

Hence, the volume of the given cone is about 150.7 cubic feet.

Example 3 :

Find the volume of the cone 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 cone.

V  =  1/3 · r²h ----- (1)

Step 2 :

To find the volume, we need the radius of the cone. But, the diameter is given, that is 15 cm. So, find the radius.

r  =  diameter / 2

r  =  15/2

r  =  7.5

Step 3 :

Plug ∏ ≈  3.14, r = 7.5 and h = 16 in (1).

≈  1/3 · 3.14 · 7.5² · 16

Simplify.

≈  1/3 · 3.14 · 56.25 · 16

≈  942

Hence, the volume of the given cone is about 942 cubic cm.

Example 4 :

Find the volume of the cone 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 cone.

V  =  1/3 · r²h

Step 2 :

Substitute the given measures.

≈  1/3 · 3.14 · 2² · 3

Simplify.

≈  1/3 · 3.14 · 4 · 3

≈  12.6

Hence, the volume of the given cone is about 12.6 cubic feet. After having gone through the stuff given above, we hope that the students would have understood "Finding the volume of a cone".