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Right circular cylinders A and B have equal volumes.
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03 Sep 2020, 02:11
03 Sep 2020, 02:11
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Question Stats:
89% (01:08) correct
10% (01:18) wrong based on 66 sessions
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Right circular cylinders A and B have equal volumes. Cylinder A has a radius of x, and cylinder B has a radius of 2x.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
The height of Cylinder A |
Twice the height of Cylinder B |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: Right circular cylinders A and B have equal volumes.
[#permalink]
03 Sep 2020, 04:28
03 Sep 2020, 04:28
1
Volume of a cylinder πr^2h
So I represent x=2 and 2x =4
Neglecting π in both sides
We have 2^2h =4^2h
Then we have 4h=16h
Then to make the equation equal
The first cylinder h must equal to 4 while the second equal to 1
In order words cylinder A height must be four times height of cylinder B
Hence Answer is QTY A
Posted from my mobile device
So I represent x=2 and 2x =4
Neglecting π in both sides
We have 2^2h =4^2h
Then we have 4h=16h
Then to make the equation equal
The first cylinder h must equal to 4 while the second equal to 1
In order words cylinder A height must be four times height of cylinder B
Hence Answer is QTY A
Posted from my mobile device
Retired Moderator
Joined: 20 Aug 2020
Posts: 49
Given Kudos: 0
Re: Right circular cylinders A and B have equal volumes.
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09 Sep 2020, 06:14
09 Sep 2020, 06:14
1
Farina wrote:
Right circular cylinders A and B have equal volumes. Cylinder A has a radius of x, and cylinder B has a radius of 2x.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
The height of Cylinder A |
Twice the height of Cylinder B |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
The formula for volumes of cylinders, rectangular solids and prisms is the product of their height and base area or \(h \cdot A\), where \(h\) is there height and \(A\) is their area, respectively.
Since a cylinder is a circle as its base, the area of its base is \(\pi r^2\) and its volume is \(\pi r^2 h\), where \(h\) and \(r\) are its height and radius, respectively.
Since cylinder \(A\) has a radius of \(x\), cylinder \(B\) has a radius of \(2x\) and they have equal volumes, we have \(\pi x^2 h_A = \pi (2x)^2 h_B\) or \(h_A = 4h_B\), where \(h_A\) and \(h_B\) are heights of those two cylinders.
Since \(h_A = 4h_B > 2h_B\), we have \(A > B\).
Therefore, A is the right answer.
