Question

a cylinder has a height of 19 millimeters. its volume is 7,218.86 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

We know that \(V = 7218.86\) cubic millimeters and \(h=19\) millimeters, and \(\pi\approx3.14\). So, \(7218.86=3.14\times r^{2}\times19\).
First, calculate \(3.14\times19 = 59.66\). Then the equation becomes \(7218.86 = 59.66r^{2}\).

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

Divide both sides of the equation \(7218.86 = 59.66r^{2}\) by \(59.66\).
\(r^{2}=\frac{7218.86}{59.66}\)
\(r^{2}=121\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r=\sqrt{121}\) or \(r = 11.00\) millimeters.

Answer:

\(11.00\)