Find the volume of the right circular cone with radius $6 \, cm$ and height $7 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^3$)

$A$ lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is $7 \,mm$ and the diameter of the graphite is $1 \,mm$. If the length of the pencil is $14 \,cm$,find the volume of the wood and that of the graphite. (in $,cm^3$)

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.

If the lateral surface area of a cylinder is $94.2 \, cm^2$ and its height is $5 \, cm$,then find the radius of its base. (in $, cm$)

Find the curved surface area of a right circular cone whose slant height is $10\, cm$ and base radius is $7\, cm$. (in $, cm^{2}$)

$A$ plastic box $1.5\, m$ long,$1.25\, m$ wide,and $65\, cm$ deep is to be made. It is opened at the top. Ignoring the thickness of the plastic sheet,determine:
$(i)$ The area of the sheet required for making the box.
$(ii)$ The cost of the sheet for it,if a sheet measuring $1\, m^2$ costs $Rs. 20$.