Question

The volume of a cube is increasing at the rate of 8 cm³/s. 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 s be the surface area of the cube.

Then, V = x³ and S = 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/s