Question

Solid A and Solid B are similar. The ratio of their volumes is 8:729. If the surface area of Solid A is 24 ft2 , what is the surface area of solid B?

Answer 1

Solids A and B appear to be similar cubes.

The volume of cube A is 8 cubic feet, so each side of cube A has length 2 feet. It follows that cube A has surface area 24 square feet. The volume of cube B is 729 cubic feet, so each side of cube B has length 9 feet. It follows that cube B has surface area (9^2) × 6 = 81 × 6 = 486 square feet.