$A$ hemisphere is made of lead. Its radius is $6 \, cm$. It is cast into a right circular cone of $75 \, cm$ height. The radius of the base of the cone is ......... $cm$.

Marbles of diameter $1.4\, cm$ are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is $7\, cm.$ Find how many marbles have been dropped in it if the water rises by $5.6\, cm.$

If the volumes of two cubes are in the ratio $27: 1$,the ratio of their edges is

Sum of the length,width and depth of a cuboid is $s$ and its diagonal is $d$. Its surface area is

$A$ field is in the form of a rectangle of length $18\, m$ and width $15\, m$. $A$ pit,$7.5\, m$ long,$6\, m$ broad and $0.8\, m$ deep,is dug in a corner of the field and the earth taken out is evenly spread over the remaining area of the field. The level of the field raised is......$cm$

$A$ 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: