The volume of the cylinder shown is $45\pi$ cubic cm. What i...
Prompt
The volume of the cylinder shown is $45\pi$ cubic cm. What is the height in centimeters of the cylinder? [asy] size(120); draw(shift(2.2,0)*yscale(0.3)*Circle((0,0), 1.2)); draw((1,0)--(1,-2)); draw((3.4,0)--(3.4,-2)); draw((1,-2)..(2.2,-2.36)..(3.4,-2)); label("$h$",midpoint((3.4,0)--(3.4,-2)),E); draw (((2.2,0)--(3.4,0))); label("$r=3$",midpoint((2.2,0)--(3.4,0)),N); [/asy]
Answer guidance
Correct answer: 5 Solution: The volume of the cylinder is $bh=\pi r^2h$. The radius of the base is $3$ cm, so we have $9\pi h=45\pi\qquad\Rightarrow h=5$. The height of the cylinder is $\boxed{5}$ cm.
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