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.
V ≈ 1/3 · 3.14 · 2² · 8
Simplify.
V ≈ 1/3 · 3.14 · 4 · 8
V ≈ 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).
V ≈ 1/3 · 3.14 · 4² · 9
Simplify.
V ≈ 1/3 · 3.14 · 16 · 9
V ≈ 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).
V ≈ 1/3 · 3.14 · 7.5² · 16
Simplify.
V ≈ 1/3 · 3.14 · 56.25 · 16
V ≈ 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.
V ≈ 1/3 · 3.14 · 2² · 3
Simplify.
V ≈ 1/3 · 3.14 · 4 · 3
V ≈ 12.6
Hence, the volume of the given cone is about 12.6 cubic feet.
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