A circular hall (i.e. cylindrical) has a hemispherical roof. The greatest height is equal to the inner diameter. If the area of the floor is equal to$k m^2$, then find the value of $k$, given that the capacity of the hall is $48510 {\mathrm{m}}^3$.

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. 

The decorative block as shown in the figure is made of two solids, a cube and a hemisphere. The base of the block is a cube with edge $5 \mathrm{cm}$ and the hemisphere fixed on the top has a diameter of $4.2 \mathrm{cm}$, then find the total surface area of the block and find the total area to be painted.

In the given figure, a solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the cone is $2 \mathrm{cm}$ and the diameter of the base is $4 \mathrm{cm}$. If a right circular cylinder circumscribes the solid, then find how much more space it will cover?