Question

The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of $2\frac{2}{3}$ cm, find the diameter of the cylinder.

Answer 1

Let R1 and R2 be the internal and external radius of the hollow spherical shells respectively.

$R_1=\frac{6}{2}=3cm$

$R_2=\frac{10}{2}=5cm$

So, volume of the hollow spherical shell

$=\frac{4}{3}\pi (R_1^3-R_2^3)$

$=\frac{4}{3}\pi (5^3-3^3)$

$=\frac{4}{3}\pi \left(98\right)c{m}^3--\left(1\right)$

Suppose r and h be the radius and height of the cylinder respectively.

$h=2\frac{2}{3}=\frac{8}{3}cm$

Volume of the cylinder = πr2h

$=\pi r^2\frac{8}{3}c{m}^3---\left(2\right)$

According to Question:–

Volume of the cylinder = Volume of the hollow spherical shell

$\pi r^2\frac{8}{3}=\frac{4}{3}\pi \left(98\right)$

$r^2\times 8=4\times 98$

$r^2=\frac{98}{2}=49$

$r=\sqrt{49}=7cm$

Hence the diameter of the cylinder

$2\times 7=14cm$