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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by M7MBA » Sun Feb 14, 2021 2:54 pm

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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

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Sun Feb 14, 2021 2:54 pm

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Re: A right circular cylinder having the radius of its base as $2$ centimeters is filled with water up to a height of

by Scott@TargetTestPrep » Tue Feb 23, 2021 5:46 am

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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