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find the maximum weight of a circular cylinder that can be cut from a spherical shot weighing 12 kilograms..
show the solution
1 Answer
- sahsjingLv 71 decade agoFavorite Answer
Equation of the sphere is
r^2+(h/2)^2 = R^2, where R is the radius of the shot, and r is the radius and h is the height of the cylinder.
Volume of the cylinder
= f(r)
= pi r^2 h
= 2pi r^2 sqrt(R^2 - r^2)
f'(r) = 0 => [2r(R^2 - r^2) - r^3] = 0
Solve for r,
r = Rsqrt(2/3)
h = 2Rsqrt(1/3)
Check: r^2+(h/2)^2 = R^2
f(Rsqrt(2/3)) = pi r^2h = 4piR^3/(3sqrt(3)), the maximum volume
the maximum weight
= [4pi R^3/(3sqrt(3))]/[(4/3)piR^3](12)
= 12sqrt(1/3)
= 6.9282 kg
