Chapter 4.1, Problem 5E

To determine

To calculate; the rate at which the height is increasing.

Answer to Problem 5E

  $\frac{dh}{dt}=0.12\text{m/min}$

Explanation of Solution

The formula of volume of a cylinder is $V=\pi r^{2}h$

By substituting the value of radius as 5:

  $V=\pi {(5)}^{2}h=25h\pi$

By differentiating on both sides:

  $\frac{d(V)}{dt}=\frac{d(25h\pi )}{dt}=25\pi \frac{dh}{dt}$

Substitute $\frac{d(V)}{dt}=3$

  $3=25\pi \frac{dh}{dt}$

  $\frac{3}{25\pi }=\frac{25\pi \frac{dh}{dt}}{25\pi }$

  $\frac{3}{25\pi }=\frac{dh}{dt}=0.12\text{m/min}$