BMSAT Kozhikode (QA) PYQs

Three small metallic cubes whose edges are in the ratio 3 : 4 : 5 are melted to form a big cube with no material lost. If the diagonal of the cube so formed is 18 cm, then the total surface area of the smallest cube (in $cm^2$) is

Water flows at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank that is $50$ m long and $44$ m wide. Determine the time in which the level of the water in the tank will rise by $7$ cm.

(Assume $\pi = 22/7$)

A pyramid rises 'h' cm from a square base of side 'a' cm to a ridge parallel to one of the base's sides, and is the same length too. What is 'h' if the volume of the pyramid is half of that of a cube of side 'a'?