Key to "The volume of a can (right circular cylinder)..."

High School
Geometry
High school geometry
Solid Geometry

nicekikah

Answered question

2021-05-14

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.

Answer & Explanation

lamusesamuset

Skilled2021-05-15Added 93 answers

The curved surface area is the circumference of the circular base times the height:
$S = C h$
$S = 2 π r h$
Given the volume of 10 cubic feet, we solve for hh in terms of rr:
$V = π r^{2} h$
$10 = π r^{2} h$

$\frac{10}{π r^{2}} = h$

Substitute to S:

$S = \frac{2 π r \times 10}{π r^{2}}$

$S = \frac{20}{r}$

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

$S r = 20$

Divide both sides by S:

$r = \frac{20}{S}$

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