12.1.23 Olympic Geometry

Condition: B the base of the quadrangular pyramid \ (s a b c d \) lies the square \ (a b c d \) with the side \ (a b = 9 \). On the continuation of the diagonal \ (c a \) for the point \ (a \) the point \ (h \) is chosen so that \ (a h = 4 c a \). The segment \ (s h = 5 \) perpendicular to the plane of the base of the pyramid. What is the largest volume \ (v \) can have a cylinder located inside the pyramid so that one of its bases lies on the basis of the pyramid? In the answer, indicate the value \ (