Question

a conical grain silo has a volume of 1,800 cubic meters and a height of 10 meters. what is the radius of the silos base? use \\( \pi = 3.14 \\). 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 \\( \square \\) meters.

Explanation:

Step1: Write the formula for the volume of 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, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know \(V = 1800\) cubic meters, \(h=10\) meters, and \(\pi = 3.14\). Substituting these into the formula gives \(1800=\frac{1}{3}\times3.14\times r^{2}\times10\).

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

First, simplify the right - hand side: \(\frac{1}{3}\times3.14\times10=\frac{31.4}{3}\approx10.47\). Then the equation becomes \(1800 = 10.47r^{2}\). Solving for \(r^{2}\), we get \(r^{2}=\frac{1800}{10.47}\approx172\).

Step4: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{172}\approx 13.1\) (rounded to the nearest tenth).

Answer:

\(13.1\)