McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
6. Surface Areas and Volumes of Spheres
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Exercise 24 Page 852

The volume of a hemisphere is half the volume of a sphere with the same radius.

49.2ft^3

Practice makes perfect

A hemisphere is the name of a solid that is half of a sphere.

Therefore, the volume of a hemisphere with radius r is half the volume of a sphere with radius r. Volume of a Hemisphere [0.8em] V=1/2(4/3π r^3) ⇔ V=2/3π r^3 To use this formula we first need to calculate the radius. To do so, we will consider the given fact that the circumference of the great circle is about 18feet. Let's recall the formula for the circumference with radius r. C=2π r We can substitute 18 for C in the above formula and solve for the radius r.

C=2Ï€ r
18=2Ï€ r
â–¼
Solve for r
9/Ï€=r
r=9/Ï€

The radius measures 9Ï€feet. We can substitute this value in the formula for the volume of a hemisphere and simplify.

V=2/3Ï€ r^3
V=2/3Ï€ ( 9/Ï€)^3
â–¼
Simplify right-hand side
V=2/3Ï€9^3/Ï€^3
V=2Ï€/39^3/Ï€^3
V=2Ï€9^3/3Ï€^3
V=1458Ï€/3Ï€^3
V=486/Ï€^2
V=49.24...
V≈ 49.2

The volume of the hemisphere to the nearest tenth is 49.2ft^3.