Question

a cone has a volume of 1441.26 cubic feet and a radius of 9 feet. what is its height? round your answer to the nearest hundredth. h ≈ feet

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of 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 \( V = 1441.26\) cubic feet and \( r=9\) feet. Substituting these into the formula \( 1441.26=\frac{1}{3}\times\pi\times9^{2}\times h \).
First, calculate \( 9^{2}=81\). Then the equation becomes \( 1441.26=\frac{1}{3}\times\pi\times81\times h \).
Since \(\frac{1}{3}\times81 = 27\), the equation simplifies to \( 1441.26=27\pi h \).

Step3: Solve for \( h \)

We know that \(\pi\approx3.14\). So, \( 1441.26=27\times3.14\times h \).
Calculate \( 27\times3.14 = 84.78\). Then \( 1441.26=84.78h \).
Divide both sides by \( 84.78\): \( h=\frac{1441.26}{84.78}\).
\( h = 17.00\)

Answer:

\(17.00\)