Video
A cylinder has a height of 11 meters. Its volume
is 11,190.96 cubic meters. What is the radius of
the cylinder?
Use л ≈ 3.14 and round your answer to the
nearest hundredth.
meters
Submit



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.