Question

janine works at a factory and is filling cylindrical molds with molten plastic. it takes 9.6 cubic centimeters of molten plastic to fill the molds to a height of 0.8 centimeters. to the nearest whole centimeter, what is the radius of the cylindrical mold?

Explanation:

Step1: Recall 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 \(V = 9.6\space cm^{3}\) and \(h=0.8\space cm\). Substituting into \(V=\pi r^{2}h\), we get \(9.6=\pi r^{2}\times0.8\).

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

First, divide both sides of the equation \(9.6=\pi r^{2}\times0.8\) by \(0.8\pi\). So \(r^{2}=\frac{9.6}{0.8\pi}\). Since \(\pi\approx3.14\), then \(r^{2}=\frac{9.6}{0.8\times3.14}=\frac{9.6}{2.512}\approx3.82\).

Step4: Solve for \(r\)

Take the square - root of \(r^{2}\). \(r=\sqrt{r^{2}}=\sqrt{3.82}\approx 2\) (rounded to the nearest whole number).

Answer:

\(2\)