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Identical hemispherical bowls of internal diameter 14 cm are to be filled with liquid from a cylindrical tank of internal diameter 40 cm and height 70 cm. If the cylindrical tank is 80% filled with liquid and the hemispherical bowls are to be filled only 75%, then how many bowls will be filled? Use π = 22/7. 

Identical hemispherical bowls of internal diameter 14 cm are to be filled with liquid from a cylindrical tank of internal diameter 40 cm and height 70 cm. If the cylindrical tank is 80% filled with liquid and the hemispherical bowls are to be filled only 75%, then how many bowls will be filled? Use π = 22/7.  Correct Answer 130

Given:

Diameter of hemisphere = 14 cm

Diameter of cylinder = 40 cm

Height of cylinder = 70 cm

Formula used:

(2/3) π × (radius)3

Calculation:

Volume of hemisphere = (2/3) π × (radius)3

⇒ Volume of one hemispherical bowl = 2/3 × 22/7 × (14/2)3 = (2156/3) cm3

∵ The bowls are to be filled only 75%,

⇒ Volume of liquid in one hemispherical bowl = 75% of (2156/3) = (3/4) × (2156/3) = 539 cm3 

Similarly,

∵ Volume of cylinder = π × (radius)2 × height 

⇒ Volume of cylindrical tank = 22/7 × (40/2)2 × 70 = 88000 cm3

∵ The tank is only 80% filled,

⇒ Volume of liquid in cylindrical tank = 80% of 88000 = 70400 cm3 

⇒ No. of hemispherical bowls that will be filled = 70400/539 = 130.62

∴ 130 hemispherical bowls will be filled 

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