The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 1023 cm. Find the diameter of the base of the cylinder.
Let the radius of the base of the cylinder be r cm.
Volume of the metallic solid cylinder of height 1023 cm = Volume of the metal in the spherical shell
⇒π×r2×323=43π(53−33)⇒323r2=43(125−27)⇒r2=332×43×98⇒r2=494⇒r=72 cm⇒d=72 ×2=7 cm
the diameter of the base of the cylinder = 7 cm.