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 15 Page 852

The surface area of a sphere is four times the product of π and the square of the radius.

127.8ft^2

Practice makes perfect

The surface area of a sphere is four times the product of π and the square of the radius. S=4π r^2We are told that the area of a circle is approximately 32 ft^2. Let's use the formula for the area A of a circle to find the radius r.

A=Ï€ r^2
32=Ï€ r^2
32/Ï€=r^2
10.18 ≈ r^2
3.19 ≈ r
r ≈ 3.19

Let's now substitute 3.19 for r in the formula for the surface area and simplify the right-hand side.

S=4Ï€ r^2
S=4Ï€ ( 3.19)^2
â–¼
Simplify right-hand side
S=4Ï€ (10.17)
S=4(10.17)Ï€
S=40.68Ï€
S=127.80...
S≈ 127.8

The surface area of the given sphere to the nearest tenth is 127.8ft^2.