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 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 ........ $cm^3$.

$A$ cylindrical vessel of radius $4 \, cm$ contains water. $A$ solid sphere of radius $3 \, cm$ is lowered into the water until it is completely immersed. The water level in the vessel will rise by (in $cm$)

Find the diagonal of a cuboid whose dimensions are $12\, m$ by $10\, m$ by $8\, m$.

$A$ cylindrical can with a horizontal base and an internal radius of $3.5 \, cm$ contains sufficient water so that when a solid sphere is placed inside,the water just covers the sphere. The sphere fits exactly into the can. The depth of the water in the can before the sphere was added 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):