Question

the volume of this cone is 157 cubic millimeters. what is the radius of this cone? round your answer to the nearest hundredth. 6 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. We know \( V = 157 \) cubic millimeters and \( h = 6 \) millimeters. We need to solve for \( r \).

Step2: Substitute the known values into the formula

Substitute \( V = 157 \) and \( h = 6 \) into the formula:
\[
157 = \frac{1}{3} \pi r^2 (6)
\]

Step3: Simplify the right - hand side of the equation

Simplify \( \frac{1}{3}\times6 = 2 \), so the equation becomes:
\[
157 = 2\pi r^2
\]

Step4: Solve for \( r^2 \)

Divide both sides of the equation by \( 2\pi \):
\[
r^2=\frac{157}{2\pi}
\]
Using \( \pi\approx3.14 \), we have \( 2\pi\approx6.28 \), then \( r^2=\frac{157}{6.28} = 25 \)

Step5: Solve for \( r \)

Take the square root of both sides: \( r=\sqrt{25}=5 \) (we take the positive square root since radius is a non - negative quantity)

Answer:

\( 5.00 \)