Question

you need to install a cylindrical wastewater holding tank outside your test lab. in the space you have available, you can install a tank with a 6 - foot diameter. you want a tank that will contain 140 cubic feet of wastewater. approximately how tall will this tank be, in feet?
a. 1
b. 4
c. 5
d. 7
e. 15

Explanation:

Step1: Find the radius

The diameter $d = 6$ feet, so the radius $r=\frac{d}{2}=\frac{6}{2}=3$ feet.

Step2: Recall the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We know $V = 140$ cubic - feet and $r = 3$ feet. We need to solve for $h$.

Step3: Rearrange the formula to solve for $h$

$h=\frac{V}{\pi r^{2}}$. Substitute $V = 140$ and $r = 3$ into the formula: $h=\frac{140}{\pi\times3^{2}}=\frac{140}{9\pi}$.

Step4: Calculate the value of $h$

$\pi\approx3.14$, so $h=\frac{140}{9\times3.14}=\frac{140}{28.26}\approx5$.

Answer:

C. 5