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# A cubic box with an edge length of 4 inches holds a ball

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Director
Joined: 05 Nov 2012
Posts: 500
Concentration: Technology, Other
A cubic box with an edge length of 4 inches holds a ball  [#permalink]

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17 Sep 2014, 10:44
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Difficulty:

55% (hard)

Question Stats:

63% (01:20) correct 37% (01:24) wrong based on 180 sessions

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A cubic box with an edge length of 4 inches holds a ball with a radius of 2 inches, such that the ball touches the box on all six sides (it is tangent to all six sides). What is the distance, in inches, between the center of the ball and a corner of the box?

A 6√3
B 4√3
C 2√3
D 2√2
E √2

Does GMAT test us on such questions?

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Math Expert
Joined: 02 Sep 2009
Posts: 47946
Re: A cubic box with an edge length of 4 inches holds a ball  [#permalink]

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17 Sep 2014, 11:39
JarvisR wrote:
A cubic box with an edge length of 4 inches holds a ball with a radius of 2 inches, such that the ball touches the box on all six sides (it is tangent to all six sides). What is the distance, in inches, between the center of the ball and a corner of the box?

A 6√3
B 4√3
C 2√3
D 2√2
E √2

Does GMAT test us on such questions?

Given that the sphere is inscribed into the cube.

The length of a diagonal of a cube equals to $$\sqrt{4^2+4^2+4^2}=4\sqrt{3}$$.

The distance between the center of the ball and a corner of the box will simply be half of the diagonal, so $$2\sqrt{3}$$.

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A cubic box with an edge length of 4 inches holds a ball  [#permalink]

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17 Sep 2014, 11:42
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Director
Joined: 05 Mar 2015
Posts: 986
Re: A cubic box with an edge length of 4 inches holds a ball  [#permalink]

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30 Jul 2016, 12:02
JarvisR wrote:
A cubic box with an edge length of 4 inches holds a ball with a radius of 2 inches, such that the ball touches the box on all six sides (it is tangent to all six sides). What is the distance, in inches, between the center of the ball and a corner of the box?

A 6√3
B 4√3
C 2√3
D 2√2
E √2

Does GMAT test us on such questions?

diagonal = √3a------>4√3
so half upto centre=2√3
Ans C

Experts please move the question in PS section...
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cube_to_sphere.gif [ 8.22 KiB | Viewed 1717 times ]

Manager
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Posts: 113
Re: A cubic box with an edge length of 4 inches holds a ball  [#permalink]

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30 Jul 2016, 13:19
When approaching this problem I noticed that the sphere touches the six edges of the box. This means I don't need additional information about the box as I already knew the radius. I also noted that calculating the distance between the center of the sphere and the corner of the box is the same thing as calculating the diagonal of a cube with each side equal to one radius of the sphere).

Given the radius of 2 I calculate the diagonal of the cube with side length 2. As the formula for the diameter of a cube is "side length*sqrt(3)". The answer had to be C. (sidelength = 2 was given in q-stem)

It would be interesting to see a question such as this one, where the test makers leave room at the top and the bottom but allow the sphere to be tangent to the up-right sides. This could likely be used in a data sufficiency question in different ways. Does anyone know about any questions like the one I described?

Best wishes.
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Intern
Joined: 24 Oct 2016
Posts: 25
Re: A cubic box with an edge length of 4 inches holds a ball  [#permalink]

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15 Oct 2017, 10:27
The distance between the center of the ball and a corner of the box is in fact half the long diagonal of this cube.

Long diagonal of a cube = s√3

so long diagonal of this particular cube is 4√3, half of which is 2√3, so C is the right answer.
Re: A cubic box with an edge length of 4 inches holds a ball &nbs [#permalink] 15 Oct 2017, 10:27
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