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Jesse Onolemen · Answer 1 · 2023-01-25T21:52:05+0000

We can write the volume of the cylinder as the product of the area of the base and its height:

$V=A_b\cdot h$

The area of the base is:

$A_b=\pi r^2$

Then, we can write the first equation and clear the height as:

$\begin{gathered} V=A_b\cdot h=\pi r^2\cdot h \\ h=(V)/(\pi r^2) \end{gathered}$

Replcing with the values V=180 cm^3 and r=3 cm, we get:

$h=\frac{180\operatorname{cm}^3}{\pi\cdot(3\operatorname{cm})^2}=\frac{180\operatorname{cm}^3}{\pi\cdot9\operatorname{cm}}\approx\frac{180\operatorname{cm}^3}{28.3\operatorname{cm}^2}=6.4\operatorname{cm}$

Answer: the height is 6.4 cm.

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