Exercise 29 Page 873

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

1708.6in^3

Practice makes perfect

The volume of a sphere is four thirds the product of π and the cube of the radius. V=4/3π r^3 Recall that the area of the great circle is the product of π and the square of the radius. A=π r^2 We are given that the area of the great circle is 55π square inches. Let's substitute the given area for A and find the radius of the sphere.

A=π r^2

Substitute

A= 55π

55π=π r^2

▼

Solve for r^2

DivEqn

.LHS /π.=.RHS /π.

55=r^2

RearrangeEqn

Rearrange equation

r^2=55

By taking the positive square root of each side we have that r= sqrt(55). Therefore, we can substitute sqrt(55) for r into the formula for the volume of a sphere to calculate V.

V=4/3π r^3

Substitute

r= sqrt(55)

V=4/3π ( sqrt(55))^3

UseCalc

Use a calculator

V=1708.56947...

RoundDec

Round to 1 decimal place(s)

V≈ 1708.6

The volume of the sphere is about 1708.6 cubic inches.