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 $5.6\, cm.$

$A$ $3.3\, m$ high room is half as long again as it is wide and its volume is $123 \frac{3}{4}\, m^3$. Find its length and breadth.

$A$ cylinder,a hemisphere,and a cone stand on the same base and have the same heights. Find the ratio of their volumes and also the ratio of the areas of their curved surfaces.

$A$ large solid sphere is melted and moulded to form identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to form a smaller solid sphere. Then the ratio of the surface area of the smaller to the surface area of the larger sphere is

Some bricks are arranged in an area measuring $20 \, m^3$. If the length, breadth, and height of each brick are $25 \, cm$, $12.5 \, cm$, and $8 \, cm$ respectively, then the number of bricks in that pile is (assume there is no gap between two bricks):

$66 \text{ cm}^3$ of silver is drawn into a wire $1 \text{ mm}$ in diameter. The length of the wire in metres will be