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

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

lamusesamuset

Skilled2021-05-15Added 93 answers

The curved surface area is the circumference of the circular base times the height:
S=Ch
S=2πrh
Given the volume of 10 cubic feet, we solve for hh in terms of rr:
V=πr2h
10=πr2h

10πr2=h

Substitute to S:

S=2πr×10πr2

S=20r

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

Sr=20

Divide both sides by S:

r=20S

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