# FINDING THE VOLUME OF A CYLINDER

## About "Finding the volume of a cylinder"

Finding the volume of a cylinder :

Finding volumes of cylinders is similar to finding volumes of prisms. We can find the volume V of both a prism and a cylinder by multiplying the height by the area of the base.

Let the area of the base of a cylinder be B and the height of the cylinder be h. Write a formula for the cylinder’s volume V.

V  =  Bh

The base of a cylinder is a circle, so for a cylinder,

B = r²

Then, we have

V  =  r²h cubic units

## Finding the volume of a cylinder - Examples

Example 1 :

Find the volume of the cylinder 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 cylinder

V  =  r²h cubic units

Step 2 :

Substitute the given measures.

≈  3.14 · 3² · 10

Simplify.

≈  3.14 · 9 · 10

≈  282.6

Hence, the volume of the given cylinder is about 282.6 cubic inches.

Example 2 :

Find the volume of the cylinder 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 cylinder

V  =  r²h cubic units ---- (1)

Step 2 :

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 6.4 cm. So, find the radius.

r  =  diameter / 2

r  =  6.4/2

r  =  3.2

Step 3 :

The given cylinder is in horizontal position and its length is 13 cm. If the cylinder is in vertical position, the length will become height. So, the height is

h  =  13

Step 4 :

Plug ∏ ≈  3.14, r = 3.2 and h = 13 in (1).

≈  3.14 · 3.2² · 13

Simplify.

≈  3.14 · 10.24 · 13

≈  418

Hence, the volume of the given cylinder is about 418 cubic cm.

Example 3 :

Find the volume of the cylinder 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 cylinder

V  =  r²h cubic units ---- (1)

Step 2 :

The given cylinder is in horizontal position and its length is 12 ft. If the cylinder is in vertical position, the length will become height. So, the height is

h  =  12

Step 3 :

Plug ∏ ≈  3.14, r = 4 and h = 12 in (1).

≈  3.14 · 4² · 12

Simplify.

≈  3.14 · 16 · 12

≈  602.9

Hence, the volume of the given cylinder is about 602.9 cubic feet.

Example 4 :

Find the volume of the cylinder 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 cylinder

V  =  r²h cubic units ---- (1)

Step 2 :

To find the volume, we need the radius of the cylinder. But, the diameter is given, that is 10 cm. So, find the radius.

r  =  diameter / 2

r  =  10/2

r  =  5

Step 2 :

Plug ∏ ≈  3.14, r = 5 and h = 6 in (1).

≈  3.14 · 5² · 6

Simplify.

≈  3.14 · 25 · 6

≈  471

Hence, the volume of the given cylinder is about 471 cubic inches. After having gone through the stuff given above, we hope that the students would have understood "Finding the volume of a cylinder".