Question

the volume of a right cone is 1728π units³. if its circumference measures 24π units, find its height. answer attempt 1 out of 2

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=24\pi\), we have \(2\pi r=24\pi\). Dividing both sides by \(2\pi\), we get \(r = 12\).

Step2: Use the volume formula to find the height

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(V = 1728\pi\) and \(r = 12\), substitute into the formula: \(1728\pi=\frac{1}{3}\pi(12)^{2}h\).
First, simplify \(\frac{1}{3}\pi(12)^{2}h=\frac{1}{3}\pi\times144h = 48\pi h\).
Then, solve the equation \(1728\pi=48\pi h\) for \(h\). Divide both sides by \(48\pi\): \(h=\frac{1728\pi}{48\pi}=36\).

Answer:

\(36\)