Problem Solving

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

GMAT assassins aren't born, they're made,
Rich

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