Find $(i)$ the curved surface area and $(ii)$ the total surface area of a hemisphere of radius $21\, cm$.

Diameter of the base of a cone is $10.5\, cm$ and its slant height is $10\, cm$. Find its curved surface area. Assume $\pi = \frac{22}{7}$. (in $, cm^2$)

$A$ dome of a building is in the form of a hemisphere. From inside,it was white-washed at the cost of $Rs. 4989.60$. If the cost of white-washing is $Rs. 20$ per square metre,find the volume of the air inside the dome. (in $, m^3$)

Monica has a piece of canvas whose area is $551 \, m^2$. She uses it to have a conical tent made,with a base radius of $7 \, m$. Assuming that all the stitching margins and the wastage incurred while cutting amounts to approximately $1 \, m^2$,find the volume of the tent that can be made with it. (in $, m^3$)

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 $m^3$.

The pillars of a temple are cylindrically shaped (see Fig.). If each pillar has a circular base of radius $20\, cm$ and height $10\, m$,how much concrete mixture would be required to build $14$ such pillars (in $, m^3$)?