FINDING THE VOLUME OF A SPHERE
About "Finding the volume of a sphere"
Finding the volume of a sphere :
We can find the volume of a sphere using the formula of volume of a cylinder.
When we model the volume of a sphere, we will be getting the following result.
Volume of cone = 2/3 · Volume of cylinder
Substitute the formula for volume of cylinder.
Volume of the cone = 2/3 · ∏r²h
A sphere always has a height which is equal to twice the radius.
So, substitute 2r for h.
Volume of sphere = 2/3 · ∏r²(2r)
Simplify.
Volume of sphere = 4/3 · ∏r³
Finding the volume of a sphere - Examples
Example 1 :
Find the volume of the sphere 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 sphere.
V = 4/3 · ∏r³
Step 2 :
Substitute the given measures.
V ≈ 4/3 · 3.14 · 2.2³
Simplify.
V ≈ 4/3 · 3.14 · 10.648
V ≈ 44.6
Hence, the volume of the given sphere is about 44.6 cubic cm.
Example 2 :
Find the volume of the sphere 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 sphere.
V = 4/3 · ∏r³ ----- (1)
Step 2 :
To find the volume, we need the radius of the sphere. But, the diameter is given, that is 42 cm. So, find the radius.
r = diameter / 2
r = 42/2
r = 21
Step 3 :
Plug ∏ ≈ 3.14 and r = 21 in (1).
V ≈ 4/3 · 3.14 · 21³
Simplify.
V ≈ 4/3 · 3.14 · 9261
V ≈ 38,772.7
Hence, the volume of the given sphere is about 38,772.7 cubic cm.
Example 3 :
Find the volume of the sphere 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 sphere.
V = 4/3 · ∏r³ ----- (1)
Step 2 :
To find the volume, we need the radius of the sphere. But, the height is given, that is 12 cm.
We know that the height of a sphere equals twice the radius.
That is,
h = 2r
Plug h = 12.
12 = 2r
Divide both sides by 2.
12/2 = 2r/2
6 = r
Step 3 :
Plug ∏ ≈ 3.14 and r = 6 in (1).
V ≈ 4/3 · 3.14 · 6³
Simplify.
V ≈ 4/3 · 3.14 · 216
V ≈ 904.3
Hence, the volume of the given sphere is about 904.3 cubic cm.
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