Question

The volume of a cube is increasing at the rate of 20 cubic centimeters per second. How fast, in square centimeters per second, is the surface area of the cube increasing at the instant when each edge of the cube is 10 centimeters long?

Answer 1

vol= l^3

dv/dt=3l^2dl/dt

20=3l^2dl/dt

when l=10 then dl/dt=20/3l^2

(dl/dt)^2= (20/3×10^2)^2