If the volume of a right circular cylinder with height $14 cm$ is $1584 c{m}^3$, then find its diameter.

If the base area of a cone is $154 c{m}^2$ and its vertical height is $15 cm$, then find its volume.

If the diameter of a sphere is $12 cm$, then find its volume.

If the diameter of a solid hemisphere is $14 cm$, then find its whole surface area.

If a side of an open cube is $75 cm$, then the length of the longest rod which can be placed in it is _____$\sqrt{3} cm$.

If the surface area of a cube is $54 c{m}^3$, then its volume is _____.

If the surface area and the volume of a cube are numerically equal, then a side of a cube is _____ units.

The surface area of a sphere of diameter $d$ is $\mathrm{\pi }\times \mathrm{d}\times$_____.

The volume of a cylinder of base diameter $10 cm$ and height $8 cm$ is _____.