Question

this cone has a volume of 65.94 cubic feet. what is its radius?
round your answer to the nearest whole number.
feet
submit

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \( V=\frac{1}{3}\pi r^{2}h\). Given \(V = 65.94\) cubic feet and \(h=7\) feet.

Step2: Substitute the values into the formula

Substitute \(V\) and \(h\) into \(V=\frac{1}{3}\pi r^{2}h\), we get \(65.94=\frac{1}{3}\times3.14\times r^{2}\times7\).
First, simplify the right - hand side: \(\frac{1}{3}\times3.14\times7=\frac{21.98}{3}\approx7.327\).
So the equation becomes \(65.94 = 7.327r^{2}\).

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

Divide both sides of the equation \(65.94 = 7.327r^{2}\) by \(7.327\): \(r^{2}=\frac{65.94}{7.327}\approx9\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\), \(r = \sqrt{9}=3\).

Answer:

\(3\)