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