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Doctors Medicines MCQs Q&A

  1. 33/14 m 
  2. 33/7 m
  3. 66/7 m
  4. 22/7 m
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1 Answers

Option 1 : 33/14 m 

Given:

Radius of cylinder, sphere, and hemisphere is equal

Height of cylindrical vessel = 14 m

Volume of cylindrical vessel = 396 m3

Formula used:

Volume of cylinder = πr2h

Volume of sphere = 4/3 π r3

Volume of hemisphere = 2/3 π r3

Calculation:

Volume of the cylinder = π × R2 × H

⇒ 396 = (22/7) × R2 × 14

⇒ R2 = (396 × 7)/ (14 × 22)

⇒ R = 3 m

Radius of each container = 3 m

Total volume of water in all three container = volume of water in the cuboidal container

Volume of cylinder + volume of sphere + volume of hemisphere = l × b × h

⇒ π × 3 × 3 × 14 + (4/3) × π × 3 × 3 × 3 + (2/3) × π × 3 × 3 × 3 = 20 × 12 × h

⇒ 9π (14 + 4 +2) = 20 × 12 × h

⇒ 9π = 12 × h

⇒ h = 33/14

∴ Water rise in cuboidal container = 33/14 m 
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