The curved surface area is the circumference of the circular base times the height:

\(S=Ch\)

\(S=2\pi rh\)

Given the volume of 10 cubic feet, we solve for hh in terms of rr:

\(\displaystyle{V}=π{r}^{{2}}{h}\)

\(\displaystyle{10}=π{r}^{{2}}{h}\)

\(\frac{10}{\pi r^2}=h\)

Substitute to S:

\(S=\frac{2\pi r\times10}{\pi r^2}\)

\(S=\frac{20}{r}\)

Solve for r in terms of S. Multiply both sides by r:

\(Sr=20\)

Divide both sides by S:

\(r=\frac{20}{S}\)