Math Problem of the Week - Algebra and Up - Feb. 20, 2022 to Feb. 26, 2022

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? You may use a calculator to solve this problem. 

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.