Question

the volume of this cone is 847.8 cubic meters. what is the radius of this cone?
round your answer to the nearest hundredth.
10 m
r ≈ meters

Explanation:

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

Step2: Substitute the known values into the formula

Given \(V = 847.8\) cubic meters and \(h=10\) meters. Substitute into \(V=\frac{1}{3}\pi r^{2}h\), we get \(847.8=\frac{1}{3}\times3.14\times r^{2}\times10\).
First, simplify the right - hand side: \(\frac{1}{3}\times3.14\times10=\frac{31.4}{3}\approx10.47\). So the equation becomes \(847.8 = 10.47r^{2}\).

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

Divide both sides of the equation \(847.8 = 10.47r^{2}\) by \(10.47\): \(r^{2}=\frac{847.8}{10.47}=81\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\), \(r=\sqrt{81}\).

Answer:

\(9.00\) meters