$A$ metal sphere of radius $20\, cm$ is melted and then cast into small hemispheres each of radius $5\, cm$. Find the number of hemispheres thus obtained (in balls).

Find the cost of digging a cuboidal pit $8 \, m$ long,$6 \, m$ broad,and $3 \, m$ deep at the rate of $Rs. 30$ per $m^3$.

$A$ right circular cylinder just encloses a sphere of radius $r$ (see figure). Find:
$(i)$ Surface area of the sphere,
$(ii)$ Curved surface area of the cylinder,
$(iii)$ Ratio of the areas obtained in $(i)$ and $(ii)$.

There are two boxes of metal sheet. The length,width,and height of a cuboidal box are $30 \, cm$,$25 \, cm$,and $20 \, cm$ respectively. $A$ cubical box has each edge of $25 \, cm$. Find out which box requires more metal sheet and by how many $cm^2$?

The length,breadth,and height of a metallic cuboid are $10\, cm$,$6\, cm$,and $4\, cm$ respectively. If the density of the metal is $7.8\, g/cm^3$,find the mass of the cuboid (in $g$).

$A$ cylindrical pillar is $50 \, cm$ in diameter and $3.5 \, m$ in height. Find the cost of painting the curved surface of the pillar at the rate of $Rs. \, 12.50$ per $m^2$. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$