Question

A cube has an edge of 2 feet. The edge is increasing at the rate of 3 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed. Hint: Remember that the volume of a cube is the cube (third power) of the length of a side.

Answer 1

36 ft³/min

Explanation:

Given that:

Let assume that length of the cube = m

Then;

m = 2 feet &;

`(dm)/(dt)= 3 \ ft/ min`

The volume (V) = m³

By differentiating with respect to t, we get

`(dV)/(dt) = 3m^2 (dm)/(dt)`

`(dV)/(dt) = 3(2)^2 * 3`

`(dV)/(dt) = 12 * 3`

= 36 ft³/min