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# What is the maximum possible volume of a cube which can be placed insi

Author Message
Intern
Joined: 25 Dec 2018
Posts: 39
Location: India
Concentration: General Management, Finance
What is the maximum possible volume of a cube which can be placed insi  [#permalink]

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02 Feb 2019, 08:39
1
00:00

Difficulty:

55% (hard)

Question Stats:

11% (00:19) correct 89% (00:47) wrong based on 9 sessions

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What is the maximum possible volume of a cube which can be placed inside a sphere with radius 10 units?(in unit3)

8000/√3
8000/(3√3)
8000√3
2400√3
1000

Kudos for every explanation
Intern
Joined: 14 May 2018
Posts: 36
GMAT 1: 710 Q49 V38
Re: What is the maximum possible volume of a cube which can be placed insi  [#permalink]

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02 Feb 2019, 10:45
3
1
mangamma wrote:
What is the maximum possible volume of a cube which can be placed inside a sphere with radius 10 units?(in unit3)

8000/√3
8000/(3√3)
8000√3
2400√3
1000

Kudos for every explanation

For maximum possible volume of a cube which can be placed inside a sphere, the diameter of the sphere must be equal to the diagonal of the sphere.

So,diagonal of cube = diameter of sphere = 20 units
diagonal of cube = a√3 ie. ==> a√3 =20 ==> a= 20/√3
Volume of cube = a^3 = (20/√3)^3 = 8000/3√3
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GMAT:710 (Q49,V38,IR8,AWA5)

Math Expert
Joined: 02 Sep 2009
Posts: 52911
Re: What is the maximum possible volume of a cube which can be placed insi  [#permalink]

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03 Feb 2019, 01:06
mangamma wrote:
What is the maximum possible volume of a cube which can be placed inside a sphere with radius 10 units?(in unit3)

8000/√3
8000/(3√3)
8000√3
2400√3
1000

Kudos for every explanation

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Re: What is the maximum possible volume of a cube which can be placed insi   [#permalink] 03 Feb 2019, 01:06
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