It costs $Rs. 2200$ to paint the inner curved surface of a cylindrical vessel $10\, m$ deep. If the cost of painting is at the rate of $Rs. 20$ per $m^2$,find the capacity of the vessel. (in $, kl$)

$A$ hemispherical bowl made of brass has an inner diameter of $10.5 \, cm$. Find the cost of tin-plating it on the inside at the rate of $Rs. 16$ per $100 \, cm^2$.

$A$ cubical box has each edge $10\, cm$ and another cuboidal box is $12.5\, cm$ long,$10\, cm$ wide and $8\, cm$ high. Which box has the greater lateral surface area and by how much (in $, cm^2$)?

$A$ 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 $,cm^3$)

Find the surface area of a sphere of diameter $21 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^{2}$)

$A$ hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is $17.6 \, m$,find the cost of painting it,given the cost of painting is $Rs. 5$ per $100 \, cm^2$.