Question

The volume of a cube is increasing at the rate of 8 cm3/*. How fast is the surface area increasing when the length of an edge is 12 cm?

Answer 1

Let x be the length of a side, V be the volume, and * be the surface area of the cube.

Then, V = x3 and * = 6x2 where x is a function of time t.

Hence, if the length of the edge of the cube is 12 cm, then the surface area is increasing at the rate of 8/3 cm2/*