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M and N are two right cylinders, such that the height of cylinder M is

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M and N are two right cylinders, such that the height of cylinder M is [#permalink] New post   28 Dec 2021, 06:37
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M and N are two right cylinders, such that the height of cylinder M is 10% greater than the height of cylinder N, and the radius of cylinder M is 10% less than the radius of cylinder N


Quantity A
Quantity B
The volume of a sphere with diameter D
The volume of a right circular cone whose height and base diameter are both D




The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
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M and N are two right cylinders, such that the height of cylinder M is [#permalink] New post   28 Dec 2021, 12:07
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Quantity A:

volume of a sphere = [4/3]*πr³ = [4/3]*π*(D/2)³ = [4/3]*π*(D³/2³) = [4D³/8*3]*π = [D³/2*3]*π = [D³/6]*π

Quantity B:

volume of a cone = [1/3]*area of the base* height = [1/3]*πr²*D = D[1/3]*(D/2)²*π = [D/3]*(D²/2²)*π = [D³/3*2²]*π = [D³/12]*π

Answer:

[D³/6]*π > [D³/12]*π

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M and N are two right cylinders, such that the height of cylinder M is [#permalink]
28 Dec 2021, 12:07
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