Question

20. The surface areas of two similar solids are 216 m² and 1014 m². The volume of the larger one is 2197 m³. What is the volume of the smaller one?

Answer 1

216 m³

Explanation:

The ratio of linear dimensions is the square root of the ratio of area dimensions.

s = √(216/1014) = √(36/169) = 6/13

Then the ratio of volume dimensions is the cube of that. The smaller volume is ...

v = (6/13)³·2197 m³ = 216/2197·2197 m³ = 216 m³

The volume of the smaller solid is 216 m³.