Question

what is the approximate volume of a cone with a height of 9 ft and radius of 3 ft? use 3.14 to approximate pi, and express your final answer to the nearest hundredth. enter your answer as a decimal in the box. \\(\square\\) ft³

Explanation:

Step1: Recall the formula for the volume 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.

Step2: Substitute the given values into the formula

We are given that \( r = 3\) ft, \( h=9\) ft and \( \pi\approx3.14 \). Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times3.14\times(3)^{2}\times9 \)
First, calculate \( (3)^{2}=9 \). Then the expression becomes:
\( V=\frac{1}{3}\times3.14\times9\times9 \)

Step3: Simplify the expression

First, \( \frac{1}{3}\times9 = 3 \). So now the expression is:
\( V=3.14\times9\times3 \)
Then, \( 9\times3=27 \). So we have:
\( V = 3.14\times27 \)
Calculating \( 3.14\times27 = 84.78 \)

Answer:

\( 84.78 \)