2015 AIME I Problems/Problem 15
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Problem
A block of wood has the shape of a right circular cylinder with radius and height
, and its entire surface has been painted blue. Points
and
are chosen on the edge of one of the circular faces of the cylinder so that
on that face measures
. The block is then sliced in half along the plane that passes through point
, point
, and the center of the cylinder, revealing a flat, unpainted face on each half. The area of one of these unpainted faces is
, where
,
, and
are integers and
is not divisible by the square of any prime. Find
.