Question

the volume of this cylinder is 19,329.84 cubic millimeters. what is the height? round your answer to the nearest hundredth. 18 mm h h ≈ millimeters

Explanation:

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

We can rewrite the formula for \(h\) as \(h = \frac{V}{\pi r^{2}}\). Given \(V = 19329.84\) cubic millimeters and \(r=18\) millimeters.
First, calculate \(r^{2}\): \(r^{2}=18^{2}=324\).
Then, substitute into the formula: \(h=\frac{19329.84}{\pi\times324}\).
Take \(\pi\approx3.14\), so \(h=\frac{19329.84}{3.14\times324}\).
Calculate \(3.14\times324 = 1017.36\).
Then \(h=\frac{19329.84}{1017.36}=19.00\).

Answer:

\(19.00\)