Question 993779: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 170 cm^3, what values of h and r will minimise the total surface area (including the top and bottom faces)?
Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
for constants h (height), r (radius), in that order.
Thank you!
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! A right circular cylinder with a given volume has the property that h = 2r where h is the height and r is the radius - this cylinder also has minimal surface area
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Volume(V) of a right circular cylinder = pi*r^2*h
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170 = pi*r^2(2*r)
170 = pi*2*r^3
r^3 = 170 / (2*pi) = 27.056340322
r = (27.056340322)^(1/3) = 3.002085229 approx 3.00
h = 2 * 3.002085229 = 6.004170458 approx 6.00
[ h, r ] = [ 6.00, 3.00 ]
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