Q60. - Algebra 1

Question

Mr. Morrison is draining his cylindrical pool. The pool has a radius of  $10 \mathrm{feet}$ and a standard height of $4.5 \mathrm{feet}.$ If the pool water is pumped out at a constant rate of  $5$ gallons per minutes, about how long will it take to drain the pool? $\left(1 {\mathrm{ft}}^3=7.5 \mathrm{gallons}\right)$

$\begin{array}{l}\mathrm{F})37.8 \min \\ \mathrm{G})7 \mathrm{h}\\ \mathrm{H})25.4 \mathrm{h}\\ \mathrm{J})35.3 \mathrm{h}\end{array}$

Step-by-Step Solution

Answer

The correct option is $\mathrm{J})35.3\text{\hspace{0.17em}h}.$ 

Step 1. Volume of a cylinder.

The basic formula to calculate the volume of cylinder with radius ‘r’ and height “h” is:  $\pi r^{2}h.$

Step 2. Volume of the pool.

Height of the pool is $4.5 \mathrm{feet}$

Radius of the pool is $10 \mathrm{feet}$ 

$\begin{array}{l}V=3.14 {\left(10 \mathrm{feet}\right)}^2 (4.5 \mathrm{feet})\\ V=1413 {\mathrm{feet}}^3\\ V=1413 \left(7.5\right)\\ V=10597.5 \mathrm{gallons}\end{array}$ 

Step 3. Time taken to drain the pool.

Rate of draining is $5$ gallons per minute.

Time taken to drain the pool is: 

$\begin{array}{l}\frac{10597.5}{5}=2119.5 \mathrm{minutes}\\ =35 \mathrm{hours} 19.5 \mathrm{minutes}.\end{array}$ 

Hence, the time taken to drain the pool is $35.3 \mathrm{hours}.$