Question

Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is `5 cm` and the volume of the cube is decreasing at a rate of `100 (cm^3)/sec`?

Answer 1

`- 4/3` cm/sec

Explanation:

`V = x^3`

`(dV)/(dt) = d/dt x^3 = 3x^2 dx/dt`

`dx/dt = (dV)/(dt) 1/ (3x^2)`

`dx/dt = - 100 * 1/ (3(5)^2) = - 4/3` cm/sec