Question

stella models a can of ground coffee as a right cylinder. she measures its height as 5 1/4 in and its volume as 8 cubic inches. find the cans diameter in inches. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the volume formula for 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. Given \(V = 8\) cubic inches and \(h=5\frac{1}{4}=\frac{21}{4}\) inches.

Step2: Substitute the values into the formula and solve for \(r\)

Substitute into \(V=\pi r^{2}h\): \(8=\pi r^{2}\times\frac{21}{4}\). First, solve for \(r^{2}\): \(r^{2}=\frac{8\times4}{21\pi}\). Then \(r^{2}=\frac{32}{21\pi}\approx\frac{32}{21\times3.14}\approx\frac{32}{65.94}\approx0.485\). So \(r=\sqrt{0.485}\approx0.7\) inches.

Step3: Find the diameter

Since the diameter \(d = 2r\), then \(d=2\times0.7 = 1.4\) inches.

Answer:

\(1.4\)