UPSC 2015 CDS II Math Paper

There are 6 faces and 4 diagonals in a cuboid.Number of right-angled triangles formed by joining the vertices of 1 face of the cuboid = 4
Number of right-angled triangles formed by joining the vertices of 6 faces of the cuboid =4×6=24Number of right-angled triangles formed by joining the vertices and 1 diagonal of the cuboid = 2
Number of right-angled triangles formed by joining the vertices and 1 diagonal of the cuboid =2×4=8
Therefore, number of right-angled triangles formed by joining the vertices of a cuboid =24+8=32