Question

the grain silo on alexas family farm is shaped like a cylinder that is 34 feet tall. when the silo is completely full, it can hold 12,000 cubic feet of grain. what is the diameter of the silo? write your answer as a whole number or decimal rounded to the nearest tenth. feet

Explanation:

Step1: Recall the volume formula of a cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height. We know that \(V = 12000\) cubic feet and \(h=34\) feet.

Step2: Solve for the radius \(r\)

Substitute the known values into the formula: \(12000=\pi r^{2}\times34\).
First, isolate \(r^{2}\): \(r^{2}=\frac{12000}{34\pi}\).
Calculate \(\frac{12000}{34\pi}\approx\frac{12000}{34\times3.14}\approx\frac{12000}{106.76}\approx112.4\).
Then, take the square - root of \(r^{2}\): \(r=\sqrt{112.4}\approx10.6\) feet.

Step3: Calculate the diameter \(d\)

Since \(d = 2r\), then \(d=2\times10.6 = 21.2\) feet.

Answer:

\(21.2\) feet