CAT (QA) PYQs

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths $10$ cm and $20$ cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is $12$ cm. If the height of the pillar is $20$ cm, then the total area, in sq cm, of all six surfaces of the pillar is

A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9 \pi$ cm$^3$. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder 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