IIM Bangalore (BBA-DBE) Geometry > Solids PYQs

A room, with a length of 18m, a height of 15 m and a total surface area of 1332 m² is to be divided into 4 m wide small rooms, by inserting plywood sheets in the room. To minimize the expenditure on the purchase of these sheets, how many 18 m × 15 m sheets will be required to construct the maximum possible number of such small rooms, if the length and the height of the small rooms remain the same as that of the original room?

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.)