CAT (QA) PYQs

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

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 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