Question

a storage tank is in the shape of a cone. it has a volume of 2,500 cubic meters and a base radius of 8 meters. find the height of the tank. use π = 3.14. round your answer to the nearest tenth.

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius of the base, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know that \(V = 2500\) cubic meters, \(r=8\) meters, and \(\pi = 3.14\). Substituting these into the formula \(V=\frac{1}{3}\pi r^{2}h\), we get \(2500=\frac{1}{3}\times3.14\times8^{2}\times h\).
First, calculate \(8^{2}=64\). Then the equation becomes \(2500=\frac{1}{3}\times3.14\times64\times h\).
Calculate \(\frac{1}{3}\times3.14\times64=\frac{3.14\times64}{3}=\frac{200.96}{3}\approx66.99\).
So the equation is \(2500 = 66.99h\).

Step3: Solve for \(h\)

To find \(h\), we use the formula \(h=\frac{V}{\frac{1}{3}\pi r^{2}}\). From \(2500 = 66.99h\), we can solve for \(h\) by \(h=\frac{2500}{66.99}\).
\(h\approx37.3\)

Answer:

The height of the tank is approximately \(37.3\) meters.