The volume of a can (right circular cylinder) is 10 cubic feet. The curved surface area is the area of the side. Write the curved surface area S as a

nicekikah 2021-05-14 Answered
The volume of a can (right circular cylinder) is 10 cubic feet. The curved surface area is the area of the side. Write the curved surface area S as a function of the radius r. Write the radius r as a function of the curved surface area S.

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Expert Answer

lamusesamuset
Answered 2021-05-15 Author has 18204 answers

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:

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

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