Question

find the volume of a cone with a base diameter of 8 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: Find the radius of the base

The diameter is 8 yd, so the radius \( r=\frac{8}{2}=4 \) yd.

Step2: Recall the volume formula for a cone

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

Step3: Substitute the values into the formula

We know \( \pi = 3.14 \), \( r = 4 \) yd, and \( h = 9 \) yd. So,
\[

$$\begin{align*} V&=\frac{1}{3}\times3.14\times4^{2}\times9\\ &=\frac{1}{3}\times3.14\times16\times9\\ &= 3.14\times16\times3\\ &= 3.14\times48 \end{align*}$$

\]

Step4: Calculate the result

\( 3.14\times48 = 150.72 \)

Answer:

\( 150.72 \) cubic yards