What is the volume (in $cm^{3}$) of a right pyramid of height $12\, cm$ and having a square base whose diagonal is $6\sqrt{2}\, cm$?

$A$ solid cone is $25 \ cm$ high and the radius of its base is $50 \ cm$. It is melted and recast into a solid sphere. Determine the surface area of the sphere (in $cm^2$).

$A$ cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio $8:5$,the ratio of their radius and height is

Volume of the cylinder is $1650\, m^3$,whereas the surface area of its base is $78 \frac{4}{7}\, m^2$. Find out the height of the cylinder (in $m$).

The volume of a right circular cone is $1232\, cm^3$ and its vertical height is $24\, cm$. Its curved surface area is.......$cm^2$.

Marbles of diameter $1.4\, cm$ are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is $7\, cm.$ Find how many marbles have been dropped in it if the water rises by $5.6\, cm.$