FINDING THE VOLUME OF A CYLINDER

Finding volumes of cylinder 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

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. 

V ≈  3.14 · 3² · 10

Simplify.

V ≈  3.14 · 9 · 10

V ≈  282.6

So, 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).

V ≈  3.14 · 3.2² · 13

Simplify.

V ≈  3.14 · 10.24 · 13

V ≈  418

So, 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). 

V ≈  3.14 · 4² · 12

Simplify.

V ≈  3.14 · 16 · 12

V ≈  602.9

So, 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). 

V ≈  3.14 · 5² · 6

Simplify.

V ≈  3.14 · 25 · 6

V ≈  471

So, the volume of the given cylinder is about 471 cubic inches. 

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