IPMAT Indore Geometry > Solids PYQs

The number of whole metallic tiles that can be produced by melting and recasting a circular metallic plate, if each of the tiles has a shape of a right-angled isosceles triangle and the circular plate has a radius equal in length to the longest side of the tile (Assume that the tiles and plate are of uniform thickness, and there is no loss of material in the melting and recasting process) is

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is $564 \ \text{cm}^2$. Then the possible values of the sum of their volumes are