BMSAT Kozhikode Geometry > Solids PYQs

A sphere fits exactly in a hollow cube. Find the ratio of the volumes of the cube and the sphere

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'?

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. $\newline$ (Assume $\pi = 22/7$)

Two solid spheres made of the same metal have weights of 5920 gm and 740 gm. If the diameter of the smaller sphere is 5 cm, then the radius of the larger sphere will be

The diameter of a solid sphere is 6 cm. If the sphere is melted and drawn into a wire of diameter 2 mm, the length of the wire will be