Question

This is a calculus question.

The volume of a cube increases at a constant rate of 10 cm^3 per second. find the rate of change in its total surface area at the instant when its when its sides are 20 cm long.

Answer 1

2 cm^2/sec

Explanation:

side of cube ---- x cm

volume = x^3

d(volume)/dt = 3x^2 dx/dt

when c = 20, d(volume)/dt = 10 cm^3/sec

10 = 3(20^2) dx/dt

dx/dt = 10/1200 = 1/120 cm/sec

Surface area = SA = 6x^2

d(SA)/dt = 12x dx/dt

so when x = 20, as above

d(SA)/dt = 12(20)(1/120) cm^2/sec

= 2 cm^2/sec