Question

given a cone with a volume of 180 cubic meters and a radius of 5 meters, which of the following will solve for the height, h?

$h = \frac{180}{(3)(5)^2\pi}$

$h = \frac{(3)(180)}{(5)^2\pi}$

$h = \frac{(2)(180)}{(5)^2\pi}$

$h = \frac{180}{(2)(5)^2\pi}$

Explanation:

Step1: Recall the volume formula 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: Solve the formula for \(h\)

Given \(V = 180\) and \(r = 5\), substitute into the formula:

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Answer:

\(h=\frac{(3)(180)}{(5)^{2}\pi}\) (the second option)