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How do you make less surface area on a cylinder whilst keeping the same volume?
Wiki User
∙ 13y ago
Volume = (area of base) x (height) = pi*r2*h
Surface area of the cylinder (think of a soup can): the top and bottom are the same; each is pi*r2, then the wall of the can unrolled is circumference of the circle times height: 2*pi*r*h.
Surface area [A] = 2*pi*r2 + 2*pi*r*h; Use the constant volume to find h in terms of V and r: h = V/(pi*r2)
A = 2*pi*r2 + 2*pi*r*V/(pi*r2) = 2*pi*r2 + 2*V*r-1
To minimize area, take derivative with respect to r, set equal to zero & solve for r.
dA/dr = 4*pi*r - 2*V*r-2 = 0 --> r3 = V/(2*pi); subst V = pi*r2*h --> r = h/2.
So the Height is twice the radius (or the height is equal to diameter).
Wiki User
∙ 13y ago
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