Question

find the volume of a cone with a height of 10 ft and a base radius of 3 ft. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume \( V \) of a cone is \( V=\frac{1}{3}\pi r^{2}h \), 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 \( r = 3\) ft, \( h=10\) ft, and \( \pi = 3.14\). Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times3.14\times(3)^{2}\times10 \)
First, calculate \( (3)^{2}=9 \). Then the expression becomes:
\( V=\frac{1}{3}\times3.14\times9\times10 \)

Step3: Simplify the expression

\( \frac{1}{3}\times9 = 3 \), so now we have \( V=3.14\times3\times10 \)
\( 3.14\times3 = 9.42 \), and then \( 9.42\times10=94.2 \)
Since the units for radius and height are in feet, the unit for volume is cubic feet (\( \text{ft}^3 \)).

Answer:

\( 94.2 \text{ ft}^3 \)