a The Spaceship Earth geosphere at Epcot is a sphere that has a diameter of 165 feet. It is similar to a typical golf ball with a diameter of approximately 1.5 inches.
We will find the volume of the Spaceship Earth using the formula of the volume of a sphere.
V=4/3π r^3
Since its diameter is 165 feet, its radius is 82.5 feet. By substituting 82.5 for r into the formula, we can find its volume. Let's do it!
The volume of the Spaceship Earth is approximately 2 352 071 ft^3.
b The diameter of the golf ball is 1.5 inches, so its radius is 0.75 inches. From here, we can find its volume proceeding in the same way as we did in Part A.
The volume of the golf ball is approximately 1.8 in^3.
c In this part we will find the scale factor from the Spaceship Earth to a golf ball. The ratio of the diameter of the Spaceship Earth to the diameter of a golf ball will give us the scale factor. Therefore, we will first convert feet to inches using the fact that 1 foot is equal to 12 inches.
165 ft * 12in./ft=1980 in.
From here, we can find the scale factor as follows.
Scale Factor
1980/1.5=1320 ⇔ 1320:1
The scale factor from the Spaceship Earth to a golf ball is 1320:1.
d To find the ratio of the volumes of Spaceship Eart to a golf ball, let's recall Theorem 12.1.
Theorem 12.1
If two similar solids have a scale factor of a:b, then the ratio of the surface areas is a^2:b^2, and the ratio of the volumes is a^3:b^3.
With this theorem, since we found that the scale factor is 1320:1, we can find the ratio of the volumes.
c|c
Scale Factor & Ratio of the Volumes
1320:1 &1320^3:1
The ratio of the volumes is 1320^3:1.
