Question

find the volume and surface area of the solid. give an exact answer and then approximate. for volume, approximate by using $\frac{22}{7}$ for $pi$ and for surface area, use 3.14 for $pi$. the exact value of the volume is (simplify your answer. type an exact answer in terms of $pi$)

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height. From the problem, we assume the radius $r = 3$ yd and height $h=9$ yd.

Step2: Calculate exact - volume

Substitute $r = 3$ and $h = 9$ into the formula:
$V=\frac{1}{3}\pi\times(3)^{2}\times9$
$V=\frac{1}{3}\pi\times9\times9$
$V = 27\pi$ cubic - yards.

Step3: Calculate approximate volume

Use $\pi=\frac{22}{7}$.
$V\approx27\times\frac{22}{7}=\frac{594}{7}=84.857$ cubic - yards (rounded to three decimal places).

Answer:

The exact value of the volume is $27\pi$ yd³.
The approximate value of the volume is $\frac{594}{7}\approx84.86$ yd³.