A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet. Express the amount A of material required to make the drum as a function of the radius r of the cylinder.
The answer is A = 2πr^2 + 200/r
Joe
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The volume of a cylinder is given by V = (pi)r^2h. So, 100 = (pi)r^2h. OR h = 100/(pi)r^2
The combined area of the top and bottom of your drum is 2(pi)r^2
The circumference of your drum is 2(pi)r
The area of the side of your drum is length times height. The length is the circumference of the drum.
So area of the side is 2(pi)r * 100/(pi)r^2 = (200(pi)r) / (pi)r^2 = 200/r.
The (pi) and an r cancel out.
So the total area is the sum of the top and bottom and the rectangle that rolls up to make the side:
A = 2(pi)r^2 + 200/r
Total surface area is 2(pi)r^2 + 100/r
Anonymous
You're just finding the surface area.
SA = 2prh + 2pr^2
I neglect to see an actual question here? You posted a statement and an answer, so I'm assuming you just want to know how it's done?