Exercise 8 Page 852

The volume of a sphere is four-thirds the product of π and the cube of the radius.

1708.6in^3

Practice makes perfect

Consider the given sphere.

The volume of a sphere is four-thirds the product of π and the cube of the radius. V=4/3π r^3 We are given the area of the great circle, 55π in^2.

Notice that the great circle and the sphere have the same radius. Let's use the formula for the area of a circle to find the radius r.

A=π r^2

A= 55π

55π=π r^2

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Solve for r

.LHS /π.=.RHS /π.

55=r^2

sqrt(LHS)=sqrt(RHS)

sqrt(55)=r

Rearrange equation

r=sqrt(55)

Let's now substitute sqrt(55) for r in the formula for the volume and simplify the right-hand side.

V=4/3π r^3

r= sqrt(55)

V=4/3π ( sqrt(55))^3

Use a calculator

V=1708.56...

Round to 1 decimal place(s)

V≈ 1708.6

The volume of the sphere to the nearest tenth is 1708.6in^3.

Exercises p.852-855

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