MathDB

Let

\mathcal{B}

be the set of rectangular boxes that have volume

23

and surface area

54

. Suppose

r

is the least possible radius of a sphere that can fit any element of

\mathcal{B}

inside it. Then

r^{2}

can be expressed as

\tfrac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p+q

Problem Statement