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