Question

amadou models a can of ground coffee as a right cylinder. he measures its height as $4\frac{1}{2}$ in and its volume as 5 cubic inches. find the cans diameter in inches. 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

Given \(V = 5\) cubic inches and \(h=4\frac{1}{2}=\frac{9}{2}\) inches. So, \(5=\pi r^{2}\times\frac{9}{2}\).

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

First, rewrite the equation as \(r^{2}=\frac{5\times2}{9\pi}\). Then \(r^{2}=\frac{10}{9\pi}\approx\frac{10}{9\times3.14}\approx\frac{10}{28.26}\approx0.354\).

Step4: Find \(r\)

Take the square - root of \(r^{2}\), \(r=\sqrt{0.354}\approx0.595\) inches.

Step5: Find the diameter \(d\)

Since \(d = 2r\), \(d=2\times0.595 = 1.19\approx1.2\) inches.

Answer:

\(1.2\) inches