Question

The radii of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of height $2\frac{2}{3}$ cm. Find the diameter of the cylinder.

Answer 1

Internal radius of the hollow spherical shell
$\left(r\right)=3cm$

and external radius$\left(R\right)=5cm\therefore Volumeofmetalused=\frac{4}{3}\pi (R^3-r^3)=\frac{4}{3}\times \pi [5^3-3^3]c{m}^3=\frac{4}{3}\pi [125-27]=\frac{98\times 4}{3}\pi c{m}^{3}Nowvolumeofcylinder=\frac{98\times 4}{3}\pi c{m}^{3}Height\left(h\right)=2\frac{2}{3}=\frac{8}{3}cm\therefore Radius=\sqrt{\frac{volume}{\pi h}}=\sqrt{\frac{98\times 4\pi \times 3}{3\times \pi \times 8}}cm=\sqrt{49}=7cm$
$\therefore$ Diameter of the cylinder $=7\times 2=14cm$