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A solid cylinder is immersed in a hemispherical bowl filled with water. What is the maximum volume of the liquid (in cubic units) that can be displaced, if the height of the cylinder is equal to the radius of the hemispherical bowl (given by r) and the radius of the cylinder is one third that of the bowl if cylinder is placed vertically?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A solid cylinder is immersed in a hemispherical bowl filled with water...
Consider the figure,
The radius of hemispherical bowl = r Radius of cylinder below the surface of water = Radius of cylinder PQRS = r/3
Height of cylinder = r
Volume of the water displaced = Volume of the cylinder immersed.
Maximum height of the cylinder that can be immersed = AB - AC = BC
Using Pythagoras theorem in ΔPOT, we get,
∴ Volume of Liquid displaced = Volume of the cylinder immersed
Hence, option 2.
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A solid cylinder is immersed in a hemispherical bowl filled with water. What is the maximum volume of the liquid (in cubic units) that can be displaced, if the height of the cylinder is equal to the radius of the hemispherical bowl (given by r) and the radius of the cylinder is one third that of the bowl if cylinder is placed vertically?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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