Answer:
Approximately \(2.7\; {\rm cm}\).
Step-by-step explanation:
If a the height of a cylinder is \(h\), and the radius of the base of the cylinder is \(r\), the volume \(V\) of the cylinder would be:
\(\displaystyle V = \pi\, r^{2}\, h\).
In this question, it is given that \(V = 190\; {\rm cm^{3}}\) and \(h = 8.5\; {\rm cm}\). Since the goal is to find base radius \(r\), rearrange the equation for \(V\) and solve for \(r\):
\(\begin{aligned}r^{2} = \frac{V}{\pi\, h}\end{aligned}\).
\(\begin{aligned}r &= \sqrt{\frac{V}{\pi\, h}} = \sqrt{\frac{190\; {\rm cm^{3}}}{(\pi)\, (8.5\; {\rm cm})}} \approx 2.7\; {\rm cm}\end{aligned}\).
In other words, the radius of the base of this cylinder would be approximately \(2.7\; {\rm cm}\).
