Question

the volume of a conical candle mold is 120 cubic centimeters, and its height is 8 centimeters. determine the radius of the base of the mold. use 3.14 for π. round off only your final answer to the nearest tenth. use the keypad to type your answer in the box provided. the radius of the base of the mold is centimeters.

Explanation:

Step1: Recall the volume formula for a cone

The volume formula for a cone is \( V=\frac{1}{3}\pi r^{2}h\), 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 \(V = 120\) cubic centimeters and \(h=8\) centimeters, and \(\pi = 3.14\). Substituting these values into the formula gives \(120=\frac{1}{3}\times3.14\times r^{2}\times8\).

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

First, simplify the right - hand side of the equation: \(\frac{1}{3}\times3.14\times8=\frac{25.12}{3}\approx8.373\). Then the equation becomes \(120 = 8.373r^{2}\). Solving for \(r^{2}\), we get \(r^{2}=\frac{120}{8.373}\approx14.33\).

Step4: Solve for \(r\)

Take the square root of \(r^{2}\): \(r=\sqrt{14.33}\approx3.8\).

Answer:

\(3.8\)