Use this picture for the problems below.

Question 1
If the radius of the shape is 9 yds and the height is 17 yards, what is the volume? Use the π
button on your calculator and round your answer to two decimal places(1 point)
volume =
yds3
Question 2
If the volume is 225 π
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)

1 answer

To help you with the questions, we will use the formula for the volume of a cylinder, which is given by:

\[ V = \pi r^2 h \]

Question 1:

Given:

  • Radius \( r = 9 \) yards
  • Height \( h = 17 \) yards

Using the formula for volume:

\[ V = \pi (9^2)(17) \]

Calculating \( 9^2 \):

\[ 9^2 = 81 \]

Then substituting back into the volume formula:

\[ V = \pi (81)(17) \]

Calculating \( 81 \times 17 \):

\[ 81 \times 17 = 1377 \]

So, we have:

\[ V = 1377 \pi \]

Now, using the π button on the calculator approximately:

\[ V \approx 1377 \times 3.14159 \approx 4324.37 \]

Thus, the volume rounded to two decimal places is:

\[ \text{Volume} \approx 4324.37 \text{ yds}^3 \]


Question 2:

We know that:

\[ V = 225 \pi \]

And we are given the radius \( r = 5 \). We need to find the height \( h \).

Using the volume formula:

\[ 225 \pi = \pi (5^2) h \]

First, simplify \( 5^2 \):

\[ 5^2 = 25 \]

So, substituting this into the equation gives:

\[ 225 \pi = \pi (25) h \]

Dividing both sides by \( \pi \) (as long as \( \pi \neq 0 \)):

\[ 225 = 25h \]

Now, solve for \( h \):

\[ h = \frac{225}{25} \]

Calculating \( \frac{225}{25} \):

\[ h = 9 \]

Thus, the height is:

\[ h = 9 \text{ (exact, no rounding needed)} \]


In summary:

  • Question 1 Answer: Volume ≈ 4324.37 yds³
  • Question 2 Answer: Height = 9 yds