CAT (QA) PYQs

A man makes complete use of $405 \mathrm{cc}$ of iron, $783 \mathrm{cc}$ of aluminium, and $351 \mathrm{cc}$ of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius $3 \mathrm{~cm}$. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is

A right circular cone, of height $12$ ft, stands on its base which has diameter $8$ ft. The tip of the cone is cut off with a plane which is parallel to the base and $9$ ft from the base. With $\pi = 22/7$, the volume, in cubic ft, of the remaining part of the cone is

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