Question

a cone has a volume of 339.12 cubic feet and a radius of 6 feet. what is its height? round your answer to the nearest hundredth. h ≈ feet submit

Explanation:

Step1: Recall the volume formula of 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 \( V = 339.12 \) cubic feet and \( r=6 \) feet, and we need to solve for \( h \).

Step2: Substitute the known values into the formula

Substitute \( V = 339.12 \), \( r = 6 \) into \( V=\frac{1}{3}\pi r^{2}h \):
\[
339.12=\frac{1}{3}\times\pi\times6^{2}\times h
\]
First, calculate \( 6^{2}=36 \), then \( \frac{1}{3}\times\pi\times36 = 12\pi\approx12\times3.14 = 37.68 \). So the equation becomes:
\[
339.12 = 37.68h
\]

Step3: Solve for \( h \)

To find \( h \), divide both sides of the equation by \( 37.68 \):
\[
h=\frac{339.12}{37.68}
\]
Calculate the division: \( \frac{339.12}{37.68} = 9 \)

Answer:

\( h\approx\boxed{9.00} \) feet (Since we need to round to the nearest hundredth, and 9 is an integer, we can write it as 9.00)