From a cubical block of wood of side $1 \, m$,a cylinder of the largest possible volume is carved out. The volume (in $m^3$) of the remaining wood is

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:

$A$ large solid sphere is melted and moulded to form identical right circular cones with base radius and height same as the radius of the sphere. One of these cones is melted and moulded to form a smaller solid sphere. Then the ratio of the surface area of the smaller to the surface area of the larger sphere is

Some bricks are arranged in an area measuring $20 \, m^3$. If the length, breadth, and height of each brick are $25 \, cm$, $12.5 \, cm$, and $8 \, cm$ respectively, then the number of bricks in that pile is (assume there is no gap between two bricks):

The diameter of a copper sphere is $18 \, cm$. The sphere is melted and drawn into a long wire of uniform circular cross-section. If the length of the wire is $108 \, m$,the diameter of the wire is ....... $cm$.

$3$ cubes of side $3, 4$ and $5$ $cm$ respectively,are melted to form a new cube. The side of the new cube is......$cm$