$A$ 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 $, m^3$)

$A$ metal pipe is $77 \, cm$ long. The inner diameter of a cross section is $4 \, cm$ and the outer diameter is $4.4 \, cm$ (see Fig.). Find its total surface area. (in $, cm^2$)

$A$ village,having a population of $4000$,requires $150$ litres of water per head per day. It has a tank measuring $20 \,m \times 15 \,m \times 6 \,m$. For how many days will the water of this tank last?

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base,using cardboard. Each penholder was to be of radius $3 \,cm$ and height $10.5 \,cm$. The Vidyalaya was to supply the competitors with cardboard. If there were $35$ competitors,how much cardboard was required to be bought for the competition (in $,cm^2$)? $\left[\text{Assume } \pi = \frac{22}{7}\right]$

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25 \,cm \times 20 \,cm \times 5 \,cm$ and the smaller of dimensions $15 \,cm \times 12 \,cm \times 5 \,cm$. For all the overlaps,$5\%$ of the total surface area is required extra. If the cost of the cardboard is $Rs. 4$ for $1000 \,cm^2$,find the cost of cardboard required for supplying $250$ boxes of each kind.

The hollow sphere,in which the circus motorcyclist performs his stunts,has a diameter of $7 \,m$. Find the area available to the motorcyclist for riding. (in $,m^2$)