Question

Water flows at 2 feet per second through a cylindrical pipe with a diameter of 8 inches.

A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.

What is the height (in inches) of water in the tank after 5 minutes?

Answer 1

Step 1: Amount of water flows in 5 minutes = water flowing per second $*5*60$

$$\begin{gathered} =1206.37\times 5\times 60 \\ =361,911{\mathrm{in}}^3 \end{gathered}$$

Diameter of collecting tank = 15 feet

Radius of collecting tank $=\frac{15}{2}feet=7.5feet=7.5\times 12=90inches$

Volume of collecting tank = $361911$

$\Rightarrow \mathrm{\pi }{\left(90\right)}^2\mathrm{h}=361911$

Step 2: Radius of collecting tank $=\frac{15}{2}\mathrm{feet}=7.5\mathrm{feet}=7.5\times 12=90\mathrm{inches}$

Volume of collecting tank = $361911$

$$\begin{gathered} \mathrm{\pi }{\left(90\right)}^2\mathrm{h}=361911 \\ \mathrm{h}=\frac{361911}{8100\times \mathrm{\pi }} \\ \mathrm{h}=14.22\mathrm{inches} \end{gathered}$$

Hence the height is about 14.22 in