$A$ solid metallic sphere of radius $21\, cm$ is melted and recast into a cone with diameter of the base as $21\, cm$. What is the height (in $cm$) of the cone?

If the sides of a triangle are doubled,its area

In the given figure,circle $P$ has a diameter of $2 \ m$ and circle $Q$ has a diameter of $1 \ m$. Find the area of the shaded region.

The area of an equilateral triangle,each of whose sides measures $2 \sqrt{3} \text{ cm}$ is

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 $ABC$?

What will be the area of a semi-$circle$ whose perimeter is $36 \, cm$? (in $cm^2$)