Answer :
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.
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.
