Chapter 12.3, Problem 23WE

To determine

To calculate: The number of minutes the tap will take to fill the reservoir

Answer to Problem 23WE

The number of minutes to fill the reservoir is $27.901$ mins

Explanation of Solution

Given information: Consider the given information,

Rate of water pouring = $1.8m^3$ per minute

  $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height

Volume = $\frac{1}{3}\pi r^{2}h$

Calculation : The height of the reservoir is,

  $h=\sqrt{{(6.8)}^2-{(\frac{5.2}{2})}^2}$

  $=\sqrt{(6.8+\frac{5.2}{2})-(6.8-\frac{5.2}{2})}$

  $=\sqrt{\frac{12}{2}\times \frac{1.6}{2}}$

  $=\sqrt{6\times 0.8}$

  $=\sqrt{\frac{48}{10}}$

  $=4\sqrt{\frac{3}{10}}$

Volume of the reservoir = $\frac{1}{3}\pi \times {(\frac{5.2}{2})}^2\times 4\sqrt{\frac{3}{10}}$ = $15.501$

Therefore, the number of minutes to fill the reservoir = $15.501\times 1.8$ = $27.901$ mins