Question

question
find the volume of a right circular cone that has a height of 11.8 ft and a base with a radius of 16 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Recall the formula for the volume of a right circular cone

The volume \( V \) of a right circular cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Substitute the given values into the formula

We are given that \( r = 16\) ft and \( h=11.8\) ft. Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times\pi\times(16)^{2}\times11.8 \)
First, calculate \( 16^{2}=256 \). Then the expression becomes:
\( V=\frac{1}{3}\times\pi\times256\times11.8 \)
Calculate \( 256\times11.8 = 256\times(10 + 1.8)=2560+460.8 = 3020.8 \)
So, \( V=\frac{1}{3}\times\pi\times3020.8 \)

Step3: Calculate the numerical value

\( \frac{1}{3}\times3020.8\approx1006.9333 \)
Then, \( V\approx1006.9333\times\pi \)
Taking \( \pi\approx3.1416 \), we have \( V\approx1006.9333\times3.1416 \approx 3163.3\) (rounded to the nearest tenth)

Answer:

\( 3163.3 \) cubic feet