All edges of a cube are expanding at the rate of 3 centimeters per second. How fast is the volume chang­ ing when each edge is (a) 1 centimeter and (b) 10 centimeters?

Answer 1

let the edge be x cm long
V = x^3
dV/dt = 3x^2 dx/dt
= 3x^2 (3) = 9x^2 cm^3/s

so when x = 1
dV/dt = 9(1) cm^3/s

do the 2nd part in the same way