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.
V ≈ 3.14 · 3² · 10
Simplify.
V ≈ 3.14 · 9 · 10
V ≈ 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).
V ≈ 3.14 · 3.2² · 13
Simplify.
V ≈ 3.14 · 10.24 · 13
V ≈ 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).
V ≈ 3.14 · 4² · 12
Simplify.
V ≈ 3.14 · 16 · 12
V ≈ 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).
V ≈ 3.14 · 5² · 6
Simplify.
V ≈ 3.14 · 25 · 6
V ≈ 471
Hence, the volume of the given cylinder is about 471 cubic inches.
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