Problem of the Week - Algebra and Up - Jan. 31, 2021 to Feb. 6, 2021

Algebra and Up: 

Question: A geography teacher has two globes in his classroom. The larger one has a volume of 972π cubic inches. If the ratio between their radii is 3:2, what is the radius of the smaller globe? 

Answer: 6 inches

Solution: 

We can solve this problem by finding the radius of the larger globe and then using the ratio between the radii to find the radius of the smaller globe. The volume of a sphere is V = ⁴/₃πr³.

972π = ⁴/₃πr³

972 = ⁴/₃r³

729 = r³

9 = r. The radius of the larger sphere is 9 inches. The ratio between the radii is 3:2. So the radius of the smaller globe must be 6 inches since 9:6 = 3:2.