A right circular cylinder having the radius of its base as \(2\) centimeters is filled with water up to a height of

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A right circular cylinder having the radius of its base as \(2\) centimeters is filled with water up to a height of \(2\) centimeters. This water is then poured into an empty rectangular container the dimensions of whose base are \(2\pi\) by \(3\) centimeters. If the volume of water in the rectangular container is increased by \(50\) percent by adding extra water, what is the final height, in centimeters, of the water level in centimeters in the rectangular container?

A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5

Answer: D

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M7MBA wrote:
Sun Feb 14, 2021 2:54 pm
A right circular cylinder having the radius of its base as \(2\) centimeters is filled with water up to a height of \(2\) centimeters. This water is then poured into an empty rectangular container the dimensions of whose base are \(2\pi\) by \(3\) centimeters. If the volume of water in the rectangular container is increased by \(50\) percent by adding extra water, what is the final height, in centimeters, of the water level in centimeters in the rectangular container?

A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5

Answer: D

Solution:

We can create the equation where h is the height of the rectangular container before the volume of the water is increased by 50%:

Volume of water in rectangular container = Volume of water in circular cylinder

2π x 3 x h = π x 2^2 x 2

6πh = 8π

h = 8π/6π = 4/3

Therefore, when the volume of the water in the rectangular container is increased by 50%, the height also increased 50% to 4/3 x 1.5 = 4/3 x 3/2 = 2 cm.

Answer: D

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