Question

A) If the radius of the shape is 9 yds and the height is 17 yards, what is the volume? Use the \
(\pi\) button on your calculator and round your answer to two decimal places (1 point)
cone

Answer 1

B) If the volume is 225\(\pi\) and the radius is 5, find the height. Round your answer to two
decimal places if necessary. You must show ALL work in order to receive full credit for the
problem. You may type your work or upload a picture. (2 points)

Answer 2

To find the volume \( V \) of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \( r \) is the radius,
- \( h \) is the height.

Given:
- The radius \( r = 9 \) yards,
- The height \( h = 17 \) yards.

Now, plug the values into the formula:

\[
V = \frac{1}{3} \pi (9)^2 (17)
\]

Calculating \( (9)^2 \):

\[
(9)^2 = 81
\]

Now substituting back into the volume formula:

\[
V = \frac{1}{3} \pi (81)(17)
\]

Calculating \( 81 \times 17 \):

\[
81 \times 17 = 1377
\]

Now, substituting this value back into the volume formula:

\[
V = \frac{1}{3} \pi (1377)
\]

Now calculate \( \frac{1}{3} \times 1377 \):

\[
\frac{1377}{3} = 459
\]

So the volume is:

\[
V = 459 \pi
\]

Now, use the \(\pi\) button on your calculator to find the numerical value. Assuming \(\pi \approx 3.14159\):

\[
V \approx 459 \times 3.14159 \approx 1444.05381
\]

Rounding to two decimal places, the volume of the cone is:

\[
\boxed{1444.05} \text{ cubic yards}
\]