Sure, let's solve the problem step-by-step.
1. Recall the formula for the volume of a cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( \pi \)[/tex] (pi) is approximately 3.14, [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height.
2. We are given:
[tex]\[
V = 11190.96 \, \text{cubic meters}
\][/tex]
[tex]\[
h = 11 \, \text{meters}
\][/tex]
[tex]\[
\pi \approx 3.14
\][/tex]
3. Rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[
V = \pi r^2 h
\][/tex]
Divide both sides by [tex]\( \pi h \)[/tex]:
[tex]\[
r^2 = \frac{V}{\pi h}
\][/tex]
So:
[tex]\[
r = \sqrt{\frac{V}{\pi h}}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
r = \sqrt{\frac{11190.96}{3.14 \times 11}}
\][/tex]
5. Calculate the denominator first:
[tex]\[
3.14 \times 11 = 34.54
\][/tex]
6. Now, divide the volume by this product:
[tex]\[
\frac{11190.96}{34.54} \approx 323.96
\][/tex]
7. Take the square root of this quotient to find the radius:
[tex]\[
r = \sqrt{323.96} \approx 18.0
\][/tex]
8. Finally, round the radius to the nearest hundredth:
[tex]\[
r \approx 18.00
\][/tex]
So, the radius of the cylinder is approximately 18.00 meters.
