Question

find the volume of a cone with a base radius of 5 yd and a height of 9 yd. 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 volume formula for 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.

Step2: Substitute the given values into the formula

We are given that \( r = 5\) yd, \( h=9\) yd, and \( \pi = 3.14\). Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times3.14\times(5)^{2}\times9 \)
First, calculate \( (5)^{2}=25 \). Then the expression becomes \( V=\frac{1}{3}\times3.14\times25\times9 \).

Step3: Simplify the expression

We can simplify \( \frac{1}{3}\times9 = 3 \). So now the expression is \( V = 3.14\times25\times3 \).
First, calculate \( 25\times3=75 \). Then, \( V=3.14\times75 \).
Calculating \( 3.14\times75 = 235.5 \).
Since the units for volume of a three - dimensional object are cubic units, and the radius and height are in yards, the unit for volume is cubic yards (\( \text{yd}^3 \)).

Answer:

\( 235.5\) cubic yards or \( 235.5\ \text{yd}^3\)