Question

The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.

SA= 576 in^2
SA= 1024 in^2
V= 2240 in^3

Answer 1

945 in²

Explanation:

The scale factor of two figures is k.

The scale factor of their surface areas is k².

The scale factor of their volumes is k³.

1024 in² / 576 in² = 16/9 = k²

k = √(16/9) = 4/3

k³ = (4/3)³

k³ = 64/27

2240 in³ × 27/64 = 945 in²