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What is the radius of the largest sphere that can be placed inside a

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What is the radius of the largest sphere that can be placed inside a  [#permalink]

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New post 08 Jan 2019, 05:07
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A
B
C
D
E

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  35% (medium)

Question Stats:

65% (00:51) correct 35% (00:40) wrong based on 22 sessions

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What is the radius of the largest sphere that can be placed inside a  [#permalink]

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New post Updated on: 08 Jan 2019, 09:20
Bunuel wrote:
What is the radius of the largest sphere that can be placed inside a cube of volume 64?


A. \(6\sqrt{2}\)

B. 8

C. 4

D. \(2\sqrt{2}\)

E. 2


a^3=64
a=4

diameter or diagnoal = 4
radius 2IMO E
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Originally posted by Archit3110 on 08 Jan 2019, 05:18.
Last edited by Archit3110 on 08 Jan 2019, 09:20, edited 1 time in total.
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Re: What is the radius of the largest sphere that can be placed inside a  [#permalink]

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New post 08 Jan 2019, 06:19
Bunuel wrote:
What is the radius of the largest sphere that can be placed inside a cube of volume 64?


A. \(6\sqrt{2}\)

B. 8

C. 4

D. \(2\sqrt{2}\)

E. 2


Volume of cube = 64 = 4^3 = Side^3
So Side = 4

A sphere will touch the cube at the centre of each face. So the length of the side of the cube will be the diameter of the sphere.
Diameter of sphere = 4
So radius of sphere = 2

Answer (E)
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Re: What is the radius of the largest sphere that can be placed inside a  [#permalink]

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New post 08 Jan 2019, 06:22
Archit3110 wrote:
Bunuel wrote:
What is the radius of the largest sphere that can be placed inside a cube of volume 64?


A. \(6\sqrt{2}\)

B. 8

C. 4

D. \(2\sqrt{2}\)

E. 2


a^3=64
a=4

diameter or diagnoal = 4sqrt2
radius 2sqrt 2IMO D


I don't think your reasoning is correct. Circle with radius \(2\sqrt{2}\) has diameter of \(4\sqrt{2}\), which is longer than the side of the cube, so the circle does not fit.

IMO ans should be 2
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Re: What is the radius of the largest sphere that can be placed inside a   [#permalink] 08 Jan 2019, 06:22
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