Question

The volumes of two similar solids are 210 m3 and 1,680 m3. The surface area of the larger solid is 856 m2.

What is the surface area of the smaller solid?

107 m2
214 m2
1034 m2
6848 m2

Answer 1

Volumes ratio = 210/1680 = 1/8, so the linear scale factor = (1/8)^(1/3) = 1/2. Surface area scales as the square of linear scale, so area ratio = (1/2)^2 = 1/4. Thus smaller surface area = 856 × 1/4 = 214 m².

Answer: 214 m².