Question

this cylinder has a volume of 785 cubic millimeters. what is its radius?
10 mm
r
round your answer to the nearest whole number.
millimeters
submit

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. Given \(V = 785\) cubic millimeters and \(h=10\) millimeters, and \(\pi\approx3.14\).

Step2: Substitute the values into the formula

Substitute \(V = 785\), \(h = 10\), and \(\pi=3.14\) into \(V=\pi r^{2}h\). We get \(785=3.14\times r^{2}\times10\).

Step3: Simplify the equation

First, simplify the right - hand side of the equation: \(3.14\times10\times r^{2}=31.4r^{2}\). So the equation becomes \(31.4r^{2}=785\).

Step4: Solve for \(r^{2}\)

Divide both sides of the equation by \(31.4\): \(r^{2}=\frac{785}{31.4}\). Calculate \(\frac{785}{31.4}=25\).

Step5: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = \sqrt{25}\).

Answer:

\(5\)