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 25 Page 852

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

77.9m^3

Practice makes perfect

Let's begin by recalling that a hemisphere is the name of a solid that is half of a sphere.

This means that 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 area of a great circle of the hemisphere is about 35m^2. A great circle is the circle that contains the center of the sphere which means that its radius is equal to the radius of the hemisphere. Let's recall the formula for the area of a circle with radius r. A=π r^2 We can substitute 35 for A in the above formula and solve for the radius r.

A=Ï€ r^2
35=Ï€ r^2
â–¼
Solve for r
35/Ï€=r^2
sqrt(35/Ï€)=r
r=sqrt(35/Ï€)

The radius measures sqrt(35Ï€)m. We can substitute this value in the formula for the volume of a hemisphere and simplify.

V=2/3Ï€ r^3
V=2/3Ï€ ( sqrt(35/Ï€))^3
V=77.881780...
V≈ 77.9

The volume of the hemisphere, to the nearest tenth, is 77.9m^3.