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# A noncompressible ball in the shape of a sphere is to be passed throug

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Math Expert
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A noncompressible ball in the shape of a sphere is to be passed throug  [#permalink]

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26 Apr 2019, 03:06
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15% (low)

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79% (00:49) correct 21% (00:49) wrong based on 57 sessions

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A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening?

(1) The radius of the ball is equal to 2 inches.
(2) The square opening is the smallest square opening through which the ball will fit.

DS64602.01
OG2020 NEW QUESTION

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A noncompressible ball in the shape of a sphere is to be passed throug  [#permalink]

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26 Apr 2019, 03:21
The radius of ball is enough to understand the perimeter of square opening as length of side of square would be equal to diameter of sphere

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Re: A noncompressible ball in the shape of a sphere is to be passed throug  [#permalink]

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27 Apr 2019, 08:10
Bunuel wrote:
A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening?

(1) The radius of the ball is equal to 2 inches.
(2) The square opening is the smallest square opening through which the ball will fit.

DS64602.01
OG2020 NEW QUESTION

#1
4/3 * pi * r^3
r=3

but we do not whether fitting of square is same/large/small to size of square
insuffcient
#2The square opening is the smallest square opening through which the ball will fit
okay we know now that vol of sphere = square area
from 1 &2
4/3 * pi * r^3 =s^2
r=2
we get s and 4s can be determined IMO C
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Re: A noncompressible ball in the shape of a sphere is to be passed throug  [#permalink]

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27 Apr 2019, 20:34
Bunuel wrote:
A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening?

(1) The radius of the ball is equal to 2 inches.
(2) The square opening is the smallest square opening through which the ball will fit.

DS64602.01
OG2020 NEW QUESTION

Let $$P$$ be the perimeter of the square opening. The original question: $$P=?$$

1) We know that the radius of the ball is $$r=2$$, but nothing can be inferred about the dimensions of the square opening. We don't even know whether the ball can pass through the opening. Thus, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

2) We know that the side length of the square opening must be equal to the diameter of the ball, but no information is given about the actual lengths. $$\implies$$ Insufficient

1&2) We know that the side length of the square opening is $$2r=2\cdot 2=4$$, so the perimeter in question is $$P=4\cdot 4=16$$. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

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Re: A noncompressible ball in the shape of a sphere is to be passed throug  [#permalink]

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15 May 2019, 20:33
Hi All,

We're told that a non-compressible ball in the shape of a SPHERE is to be passed through a SQUARE opening in a board. We're asked for the perimeter of the opening. While this question might seem a bit quirky, it's actually based on some basic Geometry rules. To start, it's worth noting that the 'widest' part of a sphere is the DIAMETER, so for the sphere to fit through a square hole, we will have to compare the diameter to the side length of the square.

(1) The radius of the ball is equal to 2 inches.

With Fact 1, we know that the diameter of the sphere is 4 inches, but we don't know anything about the square hole.
Fact 1 is INSUFFICIENT

(2) The square opening is the smallest square opening through which the ball will fit.

With Fact 2, we know that the sphere WILL fit through the hole, but we still don't know the exact perimeter of the square.
Fact 2 is INSUFFICIENT

Combined, we know...
-The radius of the ball is equal to 2 inches.
-The square opening is the smallest square opening through which the ball will fit.

We know that the square opening is as small as possible, but would still have to accommodate the diameter of 4. Thus, we have a 4x4 square and the answer to the question is 16.
Combined, SUFFICIENT

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Re: A noncompressible ball in the shape of a sphere is to be passed throug   [#permalink] 15 May 2019, 20:33
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