Asked by meysuna
Find the diameter and radius of cylinder of maximum volume which can be cut from asphere of radius 12centimeter
Answers
Answered by
Anonymous
R = sphere radius
r = cylinder radius
h = cylinder ht
draw triangle r, h/2, hypotenuse = R = 12 by the way
r^2 + (h/2)^2 = R^2
Vcylinder = (pi r^2) h
V = pi (R^2 - h^2/4)h = (pi) (R^2 h - h^3/4)
dV/dh = 0 for max or min
0 = R^2 - (3/4 )h^2
h^2 = (4/3)R^2
r = cylinder radius
h = cylinder ht
draw triangle r, h/2, hypotenuse = R = 12 by the way
r^2 + (h/2)^2 = R^2
Vcylinder = (pi r^2) h
V = pi (R^2 - h^2/4)h = (pi) (R^2 h - h^3/4)
dV/dh = 0 for max or min
0 = R^2 - (3/4 )h^2
h^2 = (4/3)R^2
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