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505-555 (Easy)|   Geometry|      
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Bunuel
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If the radius of the base of a right circular cylinder is r and its vo Updated on: 10 Jun 2021, 07:38
Originally posted by Bunuel on 10 Jun 2021, 04:45.
Last edited by Bunuel on 10 Jun 2021, 07:38, edited 1 time in total.
Edited the question.
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100% (00:51) correct 0% (00:00) wrong based on 25 sessions

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If the radius of the base of a right circular cylinder is r and its volume is \((\frac{66}{7})r^2\) cm^3, find the approximate height of the cylinder.

(A) 3 cm
(B) 4 cm
(C) 6 cm
(D) 7 cm
(E) 9 cm
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If the radius of the base of a right circular cylinder is r and its vo 10 Jun 2021, 05:10
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Bunuel
If the radius of the base of a right circular cylinder is r and its volume is \((\frac{66}{7})r^2\) cm^3, find the height of the cylinder.

(A) 3 cm
(B) 4 cm
(C) 6 cm
(D) 7 cm
(E) 9 cm
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If a right cylinder has radius r and height h, its volume is π r^2 h. So we know

π r^2 h = (66/7)r^2
π h = 66/7
π = 66/(7π)

That's not one of the answer choices. It's close in value to 3, but it is certainly not equal to 3, so there's a problem with the question design.

Recently I've seen, in more than one post on this forum, people suggesting that π = 22/7. That is not true; π is an irrational number, and cannot be expressed as a fraction of integers. This question reinforces the misconception that π is 22/7, so it's not only badly designed, it's actually counterproductive to study (it teaches math that is wrong). I'm not sure what the listed source is; I just searched for "NMAT" and only found an official GMAC product used in certain countries, but I'd be absolutely shocked to learn that a GMAC question was worded this way (not only because the answer is wrong, but because the GMAT never phrases questions in the imperative "Find the height").

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Bunuel
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