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 $cm$)

To warn ships for underwater rocks,a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of $16.5 \, km$. Find the area of the sea over which the ships are warned. (in $km^2$) (Use $\pi=3.14$)

$A$ chord of a circle of radius $10\, cm$ subtends a right angle at the centre. Find the area of the corresponding:
$(i)$ minor segment $\&$ $(ii)$ major sector. (Use $\pi=3.14$ )

Find the area of a sector of a circle with radius $6 \, cm$ if the angle of the sector is $60^{\circ}$. [use $\pi = \frac{22}{7}$]

An umbrella has $8$ ribs which are equally spaced (see $Fig.$). Assuming the umbrella to be a flat circle of radius $45 \, cm ,$ find the area between the two consecutive ribs of the umbrella. [use $\pi=\frac{22}{7}$]

On a square handkerchief,nine circular designs each of radius $7\, cm$ are made (see figure). Find the area of the remaining portion of the handkerchief. (in $cm^2$) $\left[\right.$ Use $\left.\pi=\frac{22}{7}\right]$