To find the height ([tex]\( h \)[/tex]) of a cylinder given its volume ([tex]\( V \)[/tex]) and radius ([tex]\( r \)[/tex]), we can use the formula for the volume of a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]
We are tasked with finding the height ([tex]\( h \)[/tex]) when the volume ([tex]\( V \)[/tex]) is [tex]\( 8,550 \, \text{m}^3 \)[/tex]. However, the radius ([tex]\( r \)[/tex]) is not provided in the question, which means we cannot directly compute the height without it.
Here is the step-by-step approach to solving this type of problem, assuming we had the radius value:
1. Start with the volume formula for a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]
2. Rearrange to solve for height ([tex]\( h \)[/tex]):
[tex]\[ h = \frac{V}{\pi r^2} \][/tex]
3. Substitute the given volume:
[tex]\[ V = 8,550 \, \text{m}^3 \][/tex]
4. Substitute the value of [tex]\( \pi \)[/tex] (approximately 3.14159).
Since the radius ([tex]\( r \)[/tex]) is not provided, it's essential to know the radius to find the height. If the radius is provided, use it in the formula from step 2 to find [tex]\( h \)[/tex].
So, the final answer is:
[tex]\[ \text{To find the height (\( h \)), the radius (\( r \)) must be provided.} \][/tex]
