Question

a cone - shaped grain silo has a volume of 250 cubic meters and a height of 10 meters. what is the radius of the silos base? use 3.14 for π. round your answer to the nearest tenth.
use the keypad to type your answer in the box provided.
the radius of the silos base is meters.

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for 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 \(V = 250\) cubic meters, \(h=10\) meters, and \(\pi = 3.14\). Substituting these values into the formula \(250=\frac{1}{3}\times3.14\times r^{2}\times10\).
First, simplify the right - hand side: \(\frac{1}{3}\times3.14\times10=\frac{31.4}{3}\approx10.47\). So the equation becomes \(250 = 10.47r^{2}\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(250 = 10.47r^{2}\) by \(10.47\): \(r^{2}=\frac{250}{10.47}\approx23.88\).

Step4: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{23.88}\approx4.9\).

Answer:

\(4.9\)