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

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Math Expert
Joined: 02 Sep 2009
Posts: 52279
What is the radius of the largest sphere that can be placed inside a  [#permalink]

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08 Jan 2019, 04:07
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:38) correct 35% (00:31) wrong based on 20 sessions

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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

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Joined: 18 Aug 2017
Posts: 1199
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
What is the radius of the largest sphere that can be placed inside a  [#permalink]

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Updated on: 08 Jan 2019, 08:20
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
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Originally posted by Archit3110 on 08 Jan 2019, 04:18.
Last edited by Archit3110 on 08 Jan 2019, 08:20, edited 1 time in total.
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Joined: 16 Oct 2010
Posts: 8790
Location: Pune, India
Re: What is the radius of the largest sphere that can be placed inside a  [#permalink]

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08 Jan 2019, 05:19
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

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

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08 Jan 2019, 05:22
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

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
Re: What is the radius of the largest sphere that can be placed inside a &nbs [#permalink] 08 Jan 2019, 05:22
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