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

Question

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

SamTuga · Accepted Answer

Since the side of the cube serves as the diameter of the sphere, 
2r = e
r = e/2
r = 1/2 e

Bunuel · Answer

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.

Answer: A.

Bunuel · Answer

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

AbdurRakib · Answer

Thank you very much

longhaul123 · Answer

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??

Bunuel · Answer

Yes. In geometry "inscribed" means drawing one shape inside another so that it just touches. It does not mean just inside.

SamTuga · Answer

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

ScottTargetTestPrep · Answer

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.

Answer: A

LMP · Answer

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.

graceltw · Answer

If the sphere is inscribed in a cuboid instead of a cube (i.e., sides are not of equal lengths), is it correct to say that the diameter of the sphere will be equal to the shortest length of the cuboid? Thanks!

MHIKER · Answer

As the radius of the sphere is half of the edge of the cube. The edge of the cube is  e , which equal to the diameter of the sphere. The radius  r=\frac{1}{2}e

The answer is  A .

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=3qu0jfbpUD0

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=e8puSb4RF8M

MBAHOUSE · Answer

Sometimes, at the GMAT test, is better draw the figure to visualize the math relations.
This method gives you more confidence in the measurements relations and avoid erros on easy questions like this.

bumpbot · Answer

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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

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