The radii of two cylinders are in the ratio of $2:3$ and their heights are in the ratio of $5:3$. The ratio of their volumes is

Write True or False and justify your answer in each of the following: If the length of the diagonal of a cube is $6 \sqrt{3} \, \text{cm}$,then the length of the edge of the cube is $3 \, \text{cm}$.

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

$A$ wooden bookshelf has external dimensions as follows: Height $= 110\, cm$,Depth $= 25\, cm$,Breadth $= 85\, cm$ (see Fig.). The thickness of the plank is $5\, cm$ everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $20$ paise per $cm^2$ and the rate of painting is $10$ paise per $cm^2$,find the total expenses required for polishing and painting the surface of the bookshelf.

$A$ storage tank is in the form of a cube. When it is full of water, the volume of water is $15.625 \, m^3$. If the present depth of water is $1.3 \, m$, find the volume of water already used from the tank (in $m^3$).

The radii of two cylinders are in the ratio $3:2$ and their heights are in the ratio $8:11$. The ratio of their volumes is....... .