The internal and external diameters of a hollow hemispherical vessel are $7 \mathrm{cm}$ and $14 \mathrm{cm}$ respectively. The cost of silver plating of $1 {\mathrm{cm}}^2$ surface is $₹0.60$. If the total cost of silver plating the vessel all over is $₹k$, then find the value of $k$.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is $14 \mathrm{mm}$ and the diameter of the capsule is $5 \mathrm{mm}$. If the surface area of the figure is equal to $k m{m}^2$, then find the value of $k$. [Take$\mathrm{\pi }$  = 22/7]

In the given figure, a sphere circumscribes a right cylinder whose height is $8 \mathrm{cm}$ and the radius of the base is $3 \mathrm{cm}$. Find the ratio of the volumes of the sphere and the cylinder.

A metallic cylinder has radius $3 \mathrm{cm}$ and height $5 \mathrm{cm}$. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder as shown in the figure and it is completely filled with a lighter metal B. The conical hole has a radius of $\frac{3}{2} \mathrm{cm}$ and its depth is $\frac{8}{9} \mathrm{cm}$. Calculate the ratio of the volume of the metal A to the volume of the metal B.