Inscribe Cylinder in a Sphere


While repairing an old washing machine,
Wisdom finds a cylinder balance weight needs to be replaced. In order
to save money, Wisdom decides to make this part by cutting a steel sphere.
He wants the cylinder balance weight heaviest.
What is known:
 The radius of the sphere is 0.05 m.
 The mass density of this sphere is 7,900 kg/m^{3}.
 The cylinder is inscribed in the sphere.
 The weight of the cylinder, w, is determined by its mass density,
ρ, and volume, v.
