The curved surface area of a cylinder is $550 \, cm^2$. If its height is $50 \, cm$,find its diameter in $cm$.

The volumes of two spheres are in the ratio $64: 27$. Find the ratio of their surface areas.

The radius and slant height of a conical vessel are $7 \, cm$ and $25 \, cm$ respectively. What is its capacity in litres?

The total surface area of a cube is $864 \, cm^2$. Then its edge is $\ldots \ldots \ldots \, cm$.

$A$ right triangle with sides $6 \, cm$,$8 \, cm$,and $10 \, cm$ is revolved about the side $8 \, cm$. Find the curved surface area of the solid so formed (in $cm^2$). (in $, cm^2$)

$A$ metal sphere with a radius of $12\, cm$ is melted,and recast into cones with radius $3\, cm$ and height $4\, cm$. Find how many cones are obtained?