Question

A hollow sphere of internal and external radii $6cm$ and $8cm$ respectively is melted and recast into the small cylinder of base radius $2cm$ and height $8cm$. Find the number of cylinders.

Answer 1

Volume of the hollow sphere $=\frac{4}{3}\pi R^3-\frac{4}{3}\pi r^3$

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

$=\frac{4}{3}\pi (8^3-6^3)$

$=\frac{1184\pi }{3}c{m}^3$

Volume of one small cylinder$=\pi r^{2}h=\pi \left(2^2\right)\left(8\right)$

$=32\pi c{m}^3$

Number of small cylinder formed $=\frac{\text{Volume of hollow sphere}}{\text{Volume of small cylinder}}=\frac{\frac{1184\pi }{3}}{32\pi }=\frac{37}{3}=12.33$

Hence, $12$ cylinders can be fully formed.