$A$ circular wire of radius $42 \, cm$ is cut and bent in the form of a rectangle whose sides are in the ratio $6:5$. Find the smaller side of the rectangle (in $cm$).

The heights of a cone,cylinder,and hemisphere are equal. If their radii are in the ratio $2: 3: 1$,then the ratio of their volumes is

$2$ cubes have volumes in the ratio $1:27$. The ratio of the area of the face of one to that of the other is

If $64$ buckets of water are removed from a cubical-shaped water tank completely filled with water, $1/3$ of the tank remains filled with water. The length of each side of the tank is $1.2\, m$. Assuming that all buckets are of the same measure, then the volume (in $litres$) of water contained by each bucket is:

The edges of a cuboid are in the ratio $1: 2: 3,$ and its surface area is $88 \, cm^2.$ The volume of the cuboid is ........ $cm^3$.

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