The height of a cone is $9 \, cm$. The area of the base is $1386 \, cm^2$. Find its volume (in $cm^3$).

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 surface area of a sphere is $2464 \, cm^2$. Find its diameter in $cm$.

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 $cm$)

If the total surface area of a cone is $3696 \, cm^{2}$ and the curved surface area of a cone is $2310 \, cm^{2}$,find the ratio of the radius to the slant height.

State whether the following statement is True or False and justify your answer: In a right circular cone,the height,radius,and slant height do not always form the sides of a right triangle.