A cone fits perfectly (height-wise) inside a 6 cm × 8 cm × 10 cm cuboid such that the entire base of the cone rests on one of the faces of the cuboid. Also, the circumference of the base of the cone just touches one of the pairs of the opposite sides of the face of the cuboid which is beneath it.
The volume of the cone is \( 32 \pi \, \text{cm}^3 \).