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# A sphere is inscribed in a cube with an edge of 10. What is

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A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

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23 Sep 2006, 18:24
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A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

a. 10(sqrt(3) â€“ 1)

b. 5

c. 10(sqrt(2) â€“ 1)

d. 5(sqrt(3) â€“ 1)

e. 5(sqrt(2) â€“ 1)
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23 Sep 2006, 18:40
Ill give this a crack:

assuming that the fact we are dealing with cubes and spheres makes no difference:

Need the difference between the length of the diagonal with 2 sides 10 and the diameter of the circle, then halved because there are two sections:

1/2*(10*SQRT3), then subtract the diameter of the cictle, which is 1/2*10.

so 1/2(10*SQRT3-10)
or
or 5*sqrt3-5

I think.
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23 Sep 2006, 20:47
josh478 wrote:
Ill give this a crack:

assuming that the fact we are dealing with cubes and spheres makes no difference:

Need the difference between the length of the diagonal with 2 sides 10 and the diameter of the circle, then halved because there are two sections:

1/2*(10*SQRT3), then subtract the diameter of the cictle, which is 1/2*10.

so 1/2(10*SQRT3-10)
or
or 5*sqrt3-5

I think.

josh, what I don't get is sqrt(3)

if the edge is 10, then 5^2 + 5^2=50 so hyp. of triangle = 5sqrt(2)
how do I get 5sqrt(3)?
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23 Sep 2006, 20:56
Ahh you are right, I was thinking of the wrong equation and misapplied a formula .... I was thinking the diagonal was SQRT(3) without working it out.

Of course! Thanks for the correction. I feel silly
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24 Sep 2006, 07:06
josh478 wrote:
Ahh you are right, I was thinking of the wrong equation and misapplied a formula .... I was thinking the diagonal was SQRT(3) without working it out.

Of course! Thanks for the correction. I feel silly

josh! you 5srt(3)-1 is the correct answer. you were right. I just didn't understand how to get sqrt(3) instead of sqrt(2).
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24 Sep 2006, 16:37
Nsentra wrote:
josh478 wrote:
Ahh you are right, I was thinking of the wrong equation and misapplied a formula .... I was thinking the diagonal was SQRT(3) without working it out.

Of course! Thanks for the correction. I feel silly

josh! you 5srt(3)-1 is the correct answer. you were right. I just didn't understand how to get sqrt(3) instead of sqrt(2).

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24 Sep 2006, 19:02
Nsentra wrote:
A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

a. 10(sqrt(3) â€“ 1)

b. 5

c. 10(sqrt(2) â€“ 1)

d. 5(sqrt(3) â€“ 1)

e. 5(sqrt(2) â€“ 1)

Length of solid diagonal of the cube = sqrt(10^2 + 10^2 + 10^2)
= 10sqrt(3)
Required distance = 1/2(length of solid diagonal) - radius of sphere
= 5sqrt(3) - 5

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24 Sep 2006, 19:16
Yeah. THat is what I was thinking, but didn't think it through... haha.

ok yeah,

a^2+b^2+c^2=D^2 Shortest point from one corner to an opposing corner. or the length of a diagonal of a solid rectangle.

Sometimes we get it right without proving it, I have to work on that!
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