PUMaC 2012 · 团队赛 · 第 13 题

PUMaC 2012 — Team Round — Problem 13

(3 digits) Three cones have bases on the same plane, externally tangent to each other. The cones all face the same direction. Two of the cones have radii of 2, and the other cone has a radius of 3. The two cones with radii 2 have height 4, and the other cone has height 6. Let V be the volume of the tetrahedron with three of its vertices as the three vertices of the cones 2 and the fourth vertex as the center of the base of the cone with height 6. Find V . 5 πi/ 3 2.3 Down and to the right ( e )

解析

Problem: (3 digits) Three cones have bases on the same plane, externally tangent to each other. The cones all face the same direction. Two of the cones have radii of 2, and the other cone has a radius of 3. The two cones with radii 2 have height 4, and the other cone has height