Question

The volume of a cube is increasing at a rate of 7 cm3/minute. Express the width of the cube, x, in centimeters, as a function of time t in minutes.

Thank you kindly

Answer 1

v = x^3
dv/dx = 3 x^2
dv/dt = 3 x^2 dx/dt
7 = 3 x^2 dx/dt
so
x^2 dx/dt = 7/3

Answer 2

finishing it off,
x^2 dx = 7/3 dt
1/3 x^3 = 7/3 t
x^3 = 7t
x = ∛(7t)