Question

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 $10\frac{2}{3}cm$. Find the diameter of the base of the cylinder. [4 MARKS]

Answer 1

Concept: 1 Mark
Formula: 1 Mark
Application: 2 Marks

Let the radius of the base of the cylinder be r cm.

Volume of the metallic solid cylinder of height $10\frac{2}{3}cm$ = Volume of the metal in the spherical shell

$\Rightarrow \pi \times r^2\times \frac{32}{3}=\frac{4}{3}\pi (5^3-3^3)\Rightarrow \frac{32}{3}{r}^2=\frac{4}{3}(125-27)\Rightarrow r^2=\frac{3}{32}\times \frac{4}{3}\times 98\Rightarrow r^2=\frac{49}{4}\Rightarrow r=\frac{7}{2}cm\Rightarrow d=\frac{7}{2}\times 2=7cm$