Question

a cylinder has a height of 12 millimeters. its volume is 8,478 cubic millimeters. what is the radius of the cylinder?
round your answer to the nearest hundredth.
r ≈ millimeters

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula of a cylinder is \( V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(V = 8478\) cubic millimeters and \(h=12\) millimeters. Substitute into \(V=\pi r^{2}h\), we get \(8478=\pi r^{2}\times12\).

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

First, divide both sides of the equation by \(12\pi\). \(r^{2}=\frac{8478}{12\pi}\).
Since \(\pi\approx3.14\), then \(r^{2}=\frac{8478}{12\times3.14}=\frac{8478}{37.68} = 225\).

Step4: Solve for \(r\)

Take the square root of both sides. \(r=\sqrt{225}\approx15.00\) (because \(r>0\) as it represents a radius).

Answer:

\(15.00\)