Answer:
Approximately [tex]5.6\; {\rm cm}[/tex].
Step-by-step explanation:
The volume [tex]V[/tex] of a cylinder of height [tex]h[/tex] and radius [tex]r[/tex] is [tex]V = \pi\, r^{2}\, h[/tex].
Rearrange this equation to obtain an expression for the radius [tex]r[/tex] of this cylinder:
[tex]\begin{aligned}r^{2} &= \frac{V}{\pi \, h}\end{aligned}[/tex].
[tex]\begin{aligned}r &= \sqrt{\frac{V}{\pi \, h}}\end{aligned}[/tex].
For the cylinder in this question, it is given that [tex]V = 250\; {\rm cm^{2}}[/tex] while [tex]h = 10\; {\rm cm}[/tex]. The radius of this cylinder would be:
[tex]\begin{aligned}r &= \sqrt{\frac{V}{\pi \, h}} \\ &= \sqrt{\frac{250\; {\rm cm^{3}}}{(\pi)\, (10\; {\rm cm})}} \\ &\approx 2.82\; {\rm cm} \end{aligned}[/tex].
The diameter [tex]d[/tex] of a cylinder is twice the value of radius. Thus, the diameter of this cylinder would be:
[tex]\begin{aligned} d &= 2\, r \\ &\approx (2)\, (2.82\; {\rm cm}) \\ &\approx 5.6\; {\rm cm}\end{aligned}[/tex].
