Multiple choice

Passage

Directions: Read the data carefully and answer the following question. A hollow cylindrical tank X with an inner radius of 16 cm is partially filled with water. A solid cylindrical object Y, having a radius of 9 cm and a height equal to one-fourth the height of tank X, is gently submerged into the tank such that water filled upto brim without causing any water to overflow. If the volume of water initially in the tank is 20,746 cm³.

If the radius of cylinder Y is increased by 4 cm, then how much excess amount of water would have been displaced from cylinder X?

  1. 1,396 cm3

  2. 1,696 cm3

  3. 1,936 cm3

  4. 1,693 cm3

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cylinder is pi * r^2 * h. The change in volume when the radius of cylinder Y increases from 9 cm to 13 cm is pi * h_y * (13^2 - 9^2). Given the height of Y is 1/4 of the tank's height, and the tank's inner radius is 16 cm, the displacement is based on the volume of the submerged object Y. Calculating the difference in volume for the cylinder Y with radius 13 vs 9 results in 1,936 cm^3.

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