Question

The edge of a cube is increasing at a rate of 2 inches per minute. At the instant when the volume is 27 cubic inches, how fast is the volume changing? indicate the units of measure. V=x^3

Answer 1

dx/dt = 2 inches/min
V = x^3
so,
dV/dt = 2^3 = 8 cubic inches/min

Answer 2

V = x^3
dV/dt = 3x^2 dx/dt

when V= 27, x = 3, dx/dt = 2

dV/dt = 3(3^2)(2) cubic inches/min
= 54 cubic inches/min