Question

the volume of this cylinder is 54,937.44 cubic millimeters. what is the height? round your answer to the nearest hundredth. 27 mm h h ≈ millimeters

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula for 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 known values into the formula

Given \( V = 54937.44\) \(mm^{3}\) and \( r=27\) \(mm\). First, calculate \(r^{2}=27^{2}=729\). Then the formula becomes \(54937.44=\pi\times729\times h\).

Step3: Solve for \(h\)

We know that \(\pi\approx3.14\). So, \(54937.44 = 3.14\times729\times h\). First, calculate \(3.14\times729 = 2289.06\). Then \(h=\frac{54937.44}{2289.06}\).

$$h=\frac{54937.44}{2289.06}=24.00$$

Answer:

\(24.00\)