Three metal cubes with edges $6\, cm$,$8\, cm$,and $10\, cm$ respectively are melted together and formed into a single cube. Find the side of the resulting cube (in $cm$).

In a swimming pool measuring $90\, m$ by $40\, m$,$150$ men take a dip. If the average displacement of water by a man is $8\, m^3$,what will be the rise in water level? (in $cm$)

$A$ rectangular tin sheet is $22 \ m$ long and $8 \ m$ broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder (in $m^3$) is

The length of a rectangle is increased by $33.33 \%$. By what percent should the width be decreased to maintain the same area? (in $\%$)

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?

In the given figure,$OP = PQ = 14 \, cm$ and semicircles are drawn on $OP$,$PQ$,and $OQ$ as diameters. Then,the perimeter of the shaded area is . . . . . . $cm$.