Chapter 12.8, Problem 40SPR

(a)

To determine

Find the volume of Spaceship Earth to the nearest cubic foot.

Answer to Problem 40SPR

  $2,352,071.15f{t}^3$

Explanation of Solution

Given:

The building is a sphere measuring 165 feet in diameter.A typical golf ball has a diameter of approximately 1.5 inches.

Concept Used:

The volume of a sphere is

  $V=\frac{4}{3}\pi r^3$ ; where r is the radius of the sphere.

Calculation:

The radius of the Spaceship Earth is $r=\frac{165}{2}=82.5feet$

The volume of the Spaceship Earth is $V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi {(82.5)}^3\approx 2,352,071.15f{t}^3$

(b)

To determine

Find the volume of a golf ball.

Answer to Problem 40SPR

  $1.77i{n}^3$

Explanation of Solution

Given:

The building is a sphere measuring 165 feet in diameter.A typical golf ball has a diameter of approximately 1.5 inches.

Concept Used:

The volume of a sphere is

  $V=\frac{4}{3}\pi r^3$ ; where r is the radius of the sphere.

Calculation:

The radius of the golf ball is $r=\frac{1.5}{2}=0.75inches$

The volume of the golf ball is $V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi {(0.75)}^3\approx 1.77i{n}^3$

(c)

To determine

Find the scale factor that compares Spaceship Earth and the golf ball.

Answer to Problem 40SPR

1320:1

Explanation of Solution

Given:

The building is a sphere measuring 165 feet in diameter.A typical golf ball has a diameter of approximately 1.5 inches.

Concept Used:

1 foot = 12 inches

Calculation:

First , we make the units of the diameters of Spaceship Earth and the golf ball same.

Spaceship Earth’s diameter = $165\times 12=1980in.$

The diameter of the golf ball is 1.5 inches.

The ratio of the diameters of the Spaceship Earth and the golf ball is

  $\frac{1980}{1.5}=\frac{1320}{1}$ = 1320:1

(d)

To determine

Find the ratio of volumes of the Spaceship Earth and the golf ball.

Answer to Problem 40SPR

  ${1320}^3:1^3$

Explanation of Solution

Given:

The building is a sphere measuring 165 feet in diameter.A typical golf ball has a diameter of approximately 1.5 inches.

Concept Used:

If the ratio of the measures of the two similar solids is $a:b$ , then the ratio of the volumes of the solids is $a^3:b^3$

Calculation:

From part (c) , the scaling factor of the Spaceship Earth and the golf ball is 1320:1

So, the ratio of the volumes of the Spaceship Earth and golf ball is

  ${1320}^3:1^3$