The radii of two circles are $19\, cm$ and $9\, cm$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. (in $cm$) [use $\pi=\frac{22}{7}$]

Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is

Find the area of the shaded region in the figure,where a circular arc of radius $6 \, cm$ has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side $12 \, cm$ as centre. $\left[ \text{Use } \pi = \frac{22}{7} \right]$

The area of an equilateral triangle $ABC$ is $17320.5 \, cm^2$. With each vertex of the triangle as a centre,a circle is drawn with a radius equal to half the length of the side of the triangle (see figure). Find the area of the shaded region in $cm^2$. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73205$)

The radii of two circles are $8 \, cm$ and $6 \, cm$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. [use $\pi = \frac{22}{7}$] (in $cm$)

Fig. depicts an archery target marked with its five scoring regions from the centre outwards as $Gold, Red, Blue, Black$ and $White.$ The $diameter$ of the region representing Gold score is $21\, cm$ and each of the other bands is $10.5 \,cm$ wide. Find the area of each of the five scoring regions. [use $\pi=\frac{22}{7}$]