Question

29. The ratio of the surface areas of two spheres is 1:9.

a. What is the ratio of the lengths of their radii? What is the
ratio of their volumes?

b. If the volume of the smaller sphere is 64 cubic inches, what
is the volume of the larger sphere?

Answer 1

a) 1 : 3 and 1 : 27. b) 1728 inches³

Explanation:

a) if ratio of areas is 1:9, then the ratio of lengths is √1 : √9 = 1:3

ratio of volumes is 1³ : 3³ = 1 : 27

b) volume of smaller = 64.

ratio of volumes = 1 : 27

volume of larger sphere = 27 X 64 = 1728 (inches³)