2007 iTest Problems/Problem 50

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Problem

A block $Z$ is formed by gluing one face of a solid cube with side length $6$ onto one of the circular faces of a right circular cylinder with radius $10$ and height $3$ so that the centers of the square and circle coincide. If $V$ is the smallest convex region that contains $Z$, calculate $\lfloor\operatorname{vol}V\rfloor$ (the greatest integer less than or equal to the volume of $V$).

Solution

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