Question

ella decides to estimate the volume of a coffee cup by modeling it as a right cylinder. ella measures its radius as 3 cm and its volume as 212 cubic centimeters. find the height of the cup in centimeters. round your answer to the nearest tenth if necessary.

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 given values into the formula

We know \(V = 212\) cubic centimeters and \(r=3\) centimeters. Substituting into \(V=\pi r^{2}h\), we get \(212=\pi\times(3)^{2}\times h\).

Step3: Simplify the equation

First, calculate \((3)^{2}=9\). So the equation becomes \(212 = 9\pi h\).

Step4: Solve for \(h\)

We know \(\pi\approx3.14\), then \(9\pi\approx9\times3.14 = 28.26\). The equation \(212 = 28.26h\). So \(h=\frac{212}{28.26}\approx7.5\)

Answer:

\(7.5\)