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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?
Solution
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.
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