Question

The volume V of a cube with sides of length x inches is changing with respect to time t (in seconds). When the sides of the cube are 10 in. long and increasing at the rate of 0.5 in/sec, how fast is the volume of the cube increasing?

Answer 1

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec

Explanation:

Volume V = length l^3

V = x^3

Differentiating both sides;

dV/dt = 3x^2 dv/dt

Given;

x = 10 in

dx/dt = 0.5 in/sec

dV/dt = 3×10^2 × 0.5 = 150 in^3/sec

the volume of the cube is increasing at 150in^3/sec