A cylindrical can is to have volume 1500 cubic centimeters. determine the radius and the height which will minimize the amount o

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2 years ago

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A cylindrical can is to have volume 1500 cubic centimeters. determine the radius and the height which will minimize the amount o

f material to be used. note that the surface area of a closed cylinder is s=2rh+2r2 and the volume of a cylindrical can is v=r2h.

Mathematics

1 answer:

Degger [83] · Answer 1 · 2022-06-01T20:48:21+03:00

Assuming R and H:
So volume is pir^2 * H = 1500 and H = 1500/(pir^2) while surface area is A= 2pir*H + 2pir^2
A = 2pir(r+h)= 2piR^2 + 2pir*1500/(pir^2)= 2piR^2 + 3000/r
For A to take minimum, get the derivative 4pir - 3000/R^2 and let it be 0
4pir^3 - 3000 = 0
r = cbrt(3000/(4pi)) ≈ 6.20
h = 1500/(pi(6.20)^2) ≈ 12.42