Question

a cone has a height of 16 feet and a radius of 5 feet. what is its volume? round your answer to the nearest hundredth. cubic feet

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 \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 5\) feet and \(h=16\) feet. Substitute these values into the formula: \(V=\frac{1}{3}\times\pi\times(5)^{2}\times16\).
First, calculate \((5)^{2}=25\). Then the expression becomes \(V=\frac{1}{3}\times\pi\times25\times16=\frac{400\pi}{3}\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V=\frac{400\times3.14159}{3}\).
\(400\times3.14159 = 1256.636\). Then \(V=\frac{1256.636}{3}\approx418.88\).

Answer:

\(418.88\)