OG If a sphere is inscribed in a cube

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Wed Aug 16, 2017 6:34 pm

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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 = (1/2)e

B. r = e

C. r = 2e

D. r = √e

E. r = (1/4)e^2

A

Source: Beat The GMAT — Problem Solving | Wed Aug 16, 2017 6:34 pm

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by [email protected] » Thu Aug 17, 2017 11:02 am

Hi AbeNeedsAnswers,

We're told that a sphere with radius R is inscribed in a cube with edges of length E. We're asked for an equation that correctly expresses the relationship between R and E. This is a good example of a 'concept' question (meaning that you don't have to do any significant math if you recognize the concept(s) involved.

When you INSCRIBE a sphere in a cube, that means the sphere touches ALL sides of the cube. As an example, the sphere touches the 'left side' and the 'right side' of the cube; that means the DIAMETER of the circle touches both of those sides. By extension, the diameter of the circle equals the 'edge' length of the cube.

Since the diameter is twice the radius, the radius of the sphere equals HALF of the edge of the cube (re: R = (1/2)(E))

Final Answer: A

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by Jeff@TargetTestPrep » Mon Aug 21, 2017 3:31 pm

AbeNeedsAnswers 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 = (1/2)e

B. r = e

C. r = 2e

D. r = √e

E. r = (1/4)e^2

A

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

Answer: A

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