To find the height of a cylinder given its volume and radius, we can use the formula for the volume of a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height.
Here are the given values:
- The volume [tex]\( V = 54 \pi \, \text{cm}^3 \)[/tex]
- The radius [tex]\( r = 3 \, \text{cm} \)[/tex]
We need to find the height [tex]\( h \)[/tex].
First, let's rearrange the volume formula to solve for height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{V}{\pi r^2} \][/tex]
Now plug in the given values:
[tex]\[ h = \frac{54 \pi}{\pi \cdot 3^2} \][/tex]
Simplify the expression:
[tex]\[ h = \frac{54 \pi}{\pi \cdot 9} \][/tex]
Cancel out [tex]\( \pi \)[/tex]:
[tex]\[ h = \frac{54}{9} \][/tex]
Simplify the fraction:
[tex]\[ h = 6 \][/tex]
Hence, the height of the cylinder is [tex]\( 6 \, \text{cm} \)[/tex].
Therefore, the correct answer is:
B. 6 cm
