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30

Part of 2017 Purple Comet Problems

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Purple Comet 2017 HS problem 30

Source:

3/19/2020
A container is shaped like a right circular cone with base diameter 1818 and height 1212. The vertex of the container is pointing down, and the container is open at the top. Four spheres, each with radius 33, are placed inside the container as shown. The fi rst sphere sits at the bottom and is tangent to the cone along a circle. The second, third, and fourth spheres are placed so they are each tangent to the cone and tangent to the rst sphere, and the second and fourth spheres are each tangent to the third sphere. The volume of the tetrahedron whose vertices are at the centers of the spheres is KK. Find K2K^2. https://cdn.artofproblemsolving.com/attachments/9/c/648ec2cf0f0c2f023cd00b1c0595a9396d0ddc.png
geometry3D geometry