Question

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

Answer 1

For barrel : Height = 50 cm, Radius of base = 20 cm
∴ Volume of barrel = πr²h = π × (20)² × 50 = 400 × 50 × π
For mug : Height = 15 cm, Diameter of base = 10 cm

∴ Radius of Base = 5 cm

∴ Volume of mug = πr²h = π × (5)² × 15 = 25 × 15 × π

`("Volume of barrel")/("Volume of mug") = (400 xx 50 xx pi)/(25 xx 15 xx pi) = 160/3 = 53 1/3`

∴ when 54th mug is poured in the barrel it will overflow.