To solve this problem, we need to find the radius of a cylinder given its volume and height. Here’s a step-by-step outline of how to find the radius:
### Step 1: Understand the Formula
The formula for the volume of a cylinder [tex]\( V \)[/tex] is given by:
[tex]\[ V = \pi r^2 h \][/tex]
where
- [tex]\( V \)[/tex] is the volume of the cylinder,
- [tex]\( r \)[/tex] is the radius,
- [tex]\( h \)[/tex] is the height,
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159.
### Step 2: Plug in the Known Values
From the problem, we know:
- The volume [tex]\( V \)[/tex] is 552.92 m²,
- The height [tex]\( h \)[/tex] is 11 m.
Plug these values into the formula:
[tex]\[ 552.92 = \pi r^2 \times 11 \][/tex]
### Step 3: Solve for [tex]\( r^2 \)[/tex]
First, isolate [tex]\( r^2 \)[/tex] by dividing both sides of the equation by [tex]\(\pi \times h \)[/tex]:
[tex]\[ r^2 = \frac{552.92}{\pi \times 11} \][/tex]
### Step 4: Calculate the Right Side
Let's compute the denominator:
[tex]\[ \pi \times 11 \approx 3.14159 \times 11 \approx 34.55749 \][/tex]
Now, divide the volume by this result:
[tex]\[ r^2 = \frac{552.92}{34.55749} \approx 15.999995557669582 \][/tex]
### Step 5: Take the Square Root of Both Sides
To find [tex]\( r \)[/tex], take the square root:
[tex]\[ r = \sqrt{15.999995557669582} \approx 3.9999988894173635 \][/tex]
### Step 6: Round to the Nearest Metre
Finally, round the radius to the nearest metre:
[tex]\[ r \approx 4 \][/tex]
### Conclusion
The radius of the cylinder, correct to the nearest metre, is [tex]\(\boxed{4}\)[/tex] metres.
