Question

the volume of this cone is 1,959.36 cubic millimeters. what is the radius of this cone? round your answer to the nearest hundredth. 13 mm r ≈ millimeters submit

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. From the diagram, we can see that the height \( h = 13\) mm and the volume \( V=1959.36\) cubic millimeters. We need to solve for \( r \).

First, we can rearrange the formula for \( r \). Starting with \( V=\frac{1}{3}\pi r^{2}h \), multiply both sides by 3: \( 3V=\pi r^{2}h \). Then divide both sides by \( \pi h \): \( r^{2}=\frac{3V}{\pi h} \). Then take the square root of both sides: \( r = \sqrt{\frac{3V}{\pi h}} \)

Step2: Substitute the known values

We know that \( V = 1959.36 \), \( h=13 \), and \( \pi\approx3.14 \). Substitute these values into the formula for \( r^{2} \):

\( r^{2}=\frac{3\times1959.36}{3.14\times13} \)

First, calculate the numerator: \( 3\times1959.36 = 5878.08 \)

Then calculate the denominator: \( 3.14\times13=40.82 \)

Now, divide the numerator by the denominator: \( \frac{5878.08}{40.82}\approx144 \)

Step3: Solve for \( r \)

Now that we have \( r^{2}\approx144 \), take the square root of both sides: \( r=\sqrt{144} = 12.00 \) (since radius is a positive quantity, we take the positive square root)

Answer:

\( 12.00 \)