IPMAT Rohtak 2019 (QA) PYQs

A cylindrical vessel of base radius 42 cm contains water to a certain level. A solid cylinder of height 18 cm is dropped into it and is completely submerged in water. If the level of the water in the vessel rises by 6 cm, what is the total surface area (in cm²) of the solid cylinder? (Use $\pi = \frac{22}{7}$ ) (Assuming no overflow.)

The radii of two cones are in the ratio 2:3 and their volumes are in the ratio 1:3. Then the ratio of their heights is:

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is $564 \ \text{cm}^2$. Then the possible values of the sum of their volumes are