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

The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere 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