Find the surface area of a sphere of diameter $49\, cm$ (in $cm^2$).

Write True or False and justify your answer.
$A$ right circular cylinder just encloses a sphere of radius $r$ as shown in the figure. The surface area of the sphere is equal to the curved surface area of the cylinder.

The radius and slant height of a conical vessel are $21 \,cm$ and $29 \,cm$ respectively. What is its capacity in litres?

Rain water which falls on a flat rectangular surface of length $6\, m$ and breadth $4\, m$ is transferred into a cylindrical vessel of internal radius $20\, cm$. What will be the height of water in the cylindrical vessel if the rainfall is $1\, cm$? Give your answer to the nearest integer. (Take $\pi = 3.14$) (in $cm$)

State whether the following statement is true or false:
The ratio of the surface areas of two spheres is $81: 49$. Then,the ratio of their volumes is $729: 343$.

The diameter of a solid hemisphere is $7 \, cm$. Find its curved surface area and total surface area (in $cm^2$).