The surface areas of two steel ball bearings are in the ratio $9 : 16$. What is the ratio of their volumes?

Explanation

1. 01

   Surface area goes as r², so $r_1 : r_2 = \sqrt{9} : \sqrt{16} = 3 : 4$.

2. 02

   Volume goes as r³, so the volumes are in the ratio $3^3 : 4^3 = 27 : 64$.