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? $\left(1{\mathrm{ft}}^3=7.5\mathrm{gallons}\right)$

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

Short answer

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

Step-by-step solution

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$35.3\mathrm{hours}.$