Mathematics for IGCSE & O level - Similarity (Section 1 - No. 43)

The ratio of the surface areas of two similar solids is 9:16. What is the ratio of their volumes?

3:4

9:16

27:64

81:256

Length scale factor = √9/√16 = 3/4. Hence, the volume scale factor = (3/4)³ = 27:64.