Chapter 5.6, Problem 38E

To determine

To find: the length of each edge of the cube.

Answer to Problem 38E

The length of each edge is A- $2\text{ in}\text{.}$

Explanation of Solution

Given information :

  $\frac{dv}{dt}=24\text{in}{\text{.}}^3\text{/min}\text{.}$

  $\frac{d\text{E}}{dt}=2\text{in}\text{./min}\text{.}$

Let E be the edge of each cube.

Assume all variables are differentiable function of t .

Calculation:

We have to find the length of each edge of the cube.

Therefore,

Volume of a cube-

  $\text{V}={\text{E}}^3$

Differentiate with respect to t .

  $\frac{dv}{dt}=3{\text{E}}^2\frac{d\text{E}}{dt}$

Putting the value of $\frac{dv}{dt}=24$ and $\frac{d\text{E}}{dt}=2$ in above equation,

  $\begin{array}{l}24=3{\text{E}}^2\left(2\right)\\ {\text{E}}^2=\frac{24}{3\times 2}\\ {\text{E}}^2=\frac{24}{6}\\ {\text{E}}^2=4\\ {\text{E}}^2=\sqrt{4}\\ {\text{E}}^2=2\text{in}\text{.}\end{array}$

Hence, the length of each edge is A- $2\text{ in}\text{.}$