Question

Height of a cylindrical barrel is $50$ cm and radius of its base is $20$ cm. When it was empty, Anurag started to fill the barrel with water, by a cylindrical mug. The diameter and height of the mug was $10$ cm and $15$ cm respectively. How many minimum number of mugs will be required for the barrel to overflow?

Answer 1

Given,

Height of the cylindrical barrel$=50cm$

Radius of its base$=20cm$

Height of the cylindrical mug$=15cm$

Diameter of the cylindrical mug$=10cm$

$\therefore$ Radius of the cylindrical mug$=\frac{10}{2}cm=5cm$

Volume of the cylindrical barrel$=\pi r^{2}h$

$=\pi \times (20{)}^2\times 50c{m}^3$

$=20000\pi c{m}^3$

Volume of the cylindrical mug$=\pi r^{2}h$

$=\pi \times (5{)}^2\times 15c{m}^3$

$=375\pi c{m}^3$

$\therefore$ minimum number of mugs required to fill the barrel $=\frac{volumeofbarrel}{volumeofmug}$

$=\frac{20000\pi }{375\pi }$

$=\frac{20000}{375}$

$=53.33$

Hence, the minimum number of mugs will be required for the barrel to overflow is $54$.