CAT (QA) PYQs

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1 : 8: 27: 27$. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to :

If the rectangular faces of a brick have their diagonals in the ratio $3: 2 \sqrt{3}: \sqrt{15}$, then the ratio of the length of the shortest edge of the brick to that of its longest edge is

A solid right circular cone of height $27$ cm is cut into pieces along a plane parallel to its base at a height of $18$ cm from the base. If the difference in volume of the two pieces is $225$ cc, the volume, in cc, of the original cone is