Each dimension of a cube has been increased to twice its original size. if the new cube has a volume of 64,000 cubic centimeters, what is the area of one face of the original cube?

Let x be the length of the edge of the original cube. When increased to twice its original size it becomes 2 x which gives a volume of

2x × 2x × 2x = 8x³

The volume is known. Hence

8x³ = 64,000

x³ = 8,000 which gives x = 20

The area of one face of the original (before the increase) is given by x2

x² = 20² = 400 square centimeters