An artist wishes to melt copper pennies to create a large penny proportional to an ordinary penny and with diameter 5 inches. An ordinary penny has diameter 3/4 in. How many pennies will be needed?

Question

Quizplus · Accepted Answer

The volume of a sphere (or any 3D object) scales with the cube of its linear dimensions. Since the diameter of the large penny is $ \frac{5}{\frac{3}{4}} = \frac{20}{3} $ times the diameter of an ordinary penny, the volume, and thus the amount of copper needed, will be $ \left(\frac{20}{3}\right)^3 $ times greater. An ordinary penny has a volume proportional to its diameter cubed, so $ \left(\frac{20}{3}\right)^3 \approx 296.3 $, which means approximately 300 pennies are needed.

An Artist Wishes to Melt Copper Pennies to Create a Large