Comprehension

A hollow Cylinder (C1) is full of water with a radius of 14cm and another cylinder (C2) with a radius of 7cm is placed inside the C1, then the quantity of water, which remain in the cylinder (C1) is 9240cm3. The height of both cylinders (C1) and (C2) is the same.

If the radius of cylinder (C2) increased by 3.5cm, and the height of both cylinders will remain the same, then how much quantity of water will remain in the cylinder (C1)?

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  1. 4070cm3
  2. 3850cm3
  3. 5390cm3
  4. 4850 m3
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 5390cm3
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Detailed Solution

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The volume of the Cylinder i.e. V = πr2h

According to the question:

Volume of Cylinder (C1) - Volume of Cylinder (C2) = 9240cm3

⇒ 22/7 x 14 x 14 x h - 22/7 x 7 x7 x h = 9240

⇒ 616h - 154h = 9240

⇒ 462h = 9240

⇒ h = 20cm.

New Volume of Cylinder (C2)

⇒ 22/7 x 10.5 x 10.5 x 20 cm3

⇒ 6930 cm3

Volume of Cylinder (C1) = 12320 cm3

Quantity of water remaining in cylinder (C1) = (12320 - 6930)cm3

⇒ 5390 cm3

Hence, the correct answer is 5390cm3.

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