A company sells a large globe and a small globe. The volume of the large globe is four times the volume of the small globe. The difference between the volumes is 1161.36 cubic inches. Find the radius of the small globe. Round to the nearest tenth of an inch.
A)2.3 inches
B)4.5 inches
C)10.4 inches
D)7.2 inches
E)3.6 inches

Question

Quizplus · Accepted Answer

Let the radius of the small globe be r.
Then, the radius of the large globe is 2r (twice the radius of the small globe).
Since the volume of the large globe is four times the volume of the small globe, we have:
4/3 * pi * (2r)^3 = 4 * (4/3 * pi * r^3)
Simplifying this equation, we get:
8r^3 = 16r^3 - 4645.44
8r^3 = 4645.44
r^3 = 580.68
r = 8.1 (rounded to the nearest tenth)
Therefore, the radius of the small globe is approximately 8.1 inches, which corresponds to choice B.

A Company Sells a Large Globe and a Small Globe