Write the formula to calculate the curved surface area of a frustum of a cone.

The radii of two circular ends of a frustum of a cone-shaped dustbin are $15 cm \& 8 cm.$ If its depth is $63 cm$ and the volume of the dustbin is $k c{m}^3$, then find the value of $k$.

The bottom of a right cylindrical-shaped vessel made from the metallic sheet is closed by a cone-shaped vessel as shown in the figure. The radius of the circular base of the cylinder and radius of the circular base of the cone are each is equal to $7 cm$. If the height of the cylinder is $20 cm$ and the height of the cone is $3 cm$, If the cost of milk to fill completely this vessel at the rate of Rs. $20$ per litre is $₹ k$, then find the value of $k$.

A hemispherical vessel of radius $14 cm$ is fully filled with sand. This sand is poured on level ground. The heap of sand forms a cone shape of height $7 cm$. If the area of ground occupied by the circular base of the heap of the sand is $k c{m}^2$, then find the value of $k$.

A medicine capsule is in the shape of cylinder with hemispheres stuck to each of its ends. The length of entire capsule is $14 \mathrm{mm}$ and the diameter of the capsule is $5 \mathrm{mm}$. Find its surface area.

A right circular cone of height $30 \mathrm{cm}$ is cut and removed by a plane parallel to its base from the vertex. If the volume of smaller cone obtained is $\frac{1}{27}$ of the volume of the given cone. Calculate the height of the remaining part of the cone.