The curved surface area of a cylinder is $4400 \, cm^2$ and its base has a radius of $14 \, cm$. Find the volume of the cylinder in $cm^3$.

Curved surface area of a cone $= \dots$

Write True or False and justify your answer in each of the following: $A$ cylinder and a right circular cone have the same base and the same height. The volume of the cylinder is three times the volume of the cone.

The radii of three metal spheres are $3 \,cm, 4 \,cm$ and $5 \,cm$ respectively. They are melted into a single solid sphere. Find the radius of the new solid sphere (in $cm$).

The length of a metal hollow cylinder is $70\, cm$. If the radius of the hollow inside it is $10\, cm$ and the metal thickness is $1\, cm$,find the difference between the areas of the outer and inner curved surfaces.

The slant height of a cone is $25 \,cm$ and its curved surface area is $550 \,cm^{2}$. Find the radius,height,and the total surface area of the cone.