Volume of a Cylinder

The volume of a cylinder of radius $\mathrm{r}$ is $\frac{1}{4}$ of the volume of rectangular box with a square base of side length $\mathrm{x}$. If the cylinder and the box have equal heights, what is the value of $\mathrm{r}$ in terms of $\mathrm{x}?$

Match the following.

Read the statement carefully and write 'T' for true and 'F' for false.

$\left(\mathrm{i}\right)$ Volume of a cylinder is three times the volume of a cone on the same base and of same height.

$\left(\mathrm{ii}\right)$ Volume of boggest sphere in cube of edge $6 \mathrm{cm}$ is $36\mathrm{\pi } {\mathrm{cm}}^3$.

$\left(\mathrm{iii}\right)$ Cuboids and cubes are special forms of right prisms.

A school provides milk to the students daily in a cylindrical glasses of diameter $7\mathrm{cm}$. If the glass is filled with milk upto an height of $12 \mathrm{cm},$ then how many litres of milk is needed to serve $1600$students?

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

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?