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# If a sphere with radius r is inscribed in a cube with edges of length

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If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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Updated on: 17 Jun 2017, 13:49
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If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. $$r=\frac{1}{2}e$$

B. r = e

C. r = 2e

D. $$r=\sqrt{e}$$

E. $$r=\frac{1}{4}e^2$$

Originally posted by AbdurRakib on 17 Jun 2017, 11:06.
Last edited by Bunuel on 17 Jun 2017, 13:49, edited 1 time in total.
Edited the question.
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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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05 Jul 2017, 08:30
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Since the side of the cube serves as the diameter of the sphere,
2r = e
r = e/2
r = 1/2 e
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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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17 Jun 2017, 13:55
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AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. $$r=\frac{1}{2}e$$

B. r = e

C. r = 2e

D. $$r=\sqrt{e}$$

E. $$r=\frac{1}{4}e^2$$

A sphere inscribed in a cube has the diameter equal to the edge of the cube. Thus, 2r = s, which is the same as r = s/2.

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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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17 Jun 2017, 13:56
Bunuel wrote:
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. $$r=\frac{1}{2}e$$

B. r = e

C. r = 2e

D. $$r=\sqrt{e}$$

E. $$r=\frac{1}{4}e^2$$

A sphere inscribed in a cube has the diameter equal to the edge of the cube. Thus, 2r = s, which is the same as r = s/2.

Check other 3-D Geometry Questions in our Special Questions Directory.
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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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17 Jun 2017, 14:01
Top Contributor
Bunuel wrote:
Bunuel wrote:
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. $$r=\frac{1}{2}e$$

B. r = e

C. r = 2e

D. $$r=\sqrt{e}$$

E. $$r=\frac{1}{4}e^2$$

A sphere inscribed in a cube has the diameter equal to the edge of the cube. Thus, 2r = s, which is the same as r = s/2.

Check other 3-D Geometry Questions in our Special Questions Directory.

Thank you very much
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If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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16 Jul 2017, 04:22
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square . Am i correct??
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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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16 Jul 2017, 04:28
longhaul123 wrote:
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square . Am i correct??

Yes. In geometry "inscribed" means drawing one shape inside another so that it just touches. It does not mean just inside.
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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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16 Jul 2017, 07:43
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longhaul123 wrote:
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square. Am I correct??

Sure the inscribed circle must touch all the four sides of the Rectangle so the side of the rectangle is same as the diameter. see the images attached that also show circumscribed circle, in this case the diagonal of the rectangle serves and the diameter
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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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15 Nov 2017, 16:50
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AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. $$r=\frac{1}{2}e$$

B. r = e

C. r = 2e

D. $$r=\sqrt{e}$$

E. $$r=\frac{1}{4}e^2$$

Since the sphere is inscribed in the cube, the length of an edge of the cube = the diameter of the sphere. Recall that the diameter is twice the radius. Thus, e = 2r, or 1/2e = r.

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Re: If a sphere with radius r is inscribed in a cube with edges of length  [#permalink]

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23 Jun 2019, 06:44
AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?

A. $$r=\frac{1}{2}e$$

B. r = e

C. r = 2e

D. $$r=\sqrt{e}$$

E. $$r=\frac{1}{4}e^2$$

First of all, if you have a sphere that is inscribed inside of a cube,

that means that the cube's side is going to be exactly twice the radius.

So the radius is going to be half of the edge, and that's about it.

You don't need to calculate anything. The correct answer choice is A.
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Re: If a sphere with radius r is inscribed in a cube with edges of length   [#permalink] 23 Jun 2019, 06:44
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