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

Answer:

36  ft³/min

Step-by-step explanation:

Given that:

Let assume that length of the cube = m

Then;

m = 2 feet  &;

$\dfrac{dm}{dt}= 3 \ ft/ min$

The volume (V) = m³

By differentiating with respect to t, we get

$\dfrac{dV}{dt} = 3m^2 \dfrac{dm}{dt}$

$\dfrac{dV}{dt} = 3(2)^2 \times 3$

$\dfrac{dV}{dt} = 12 \times 3$

= 36 ft³/min