The diameter of a coin is $1 \mathrm{cm}$ (Fig. $13.49$). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take $\mathrm{\pi }= 3.1416$).

    

In Fig., $\mathrm{AB}$ and $\mathrm{CD}$ are two diameters of a circle perpendicular to each other and $\mathrm{OD}$ is the diameter of the smaller circle. If$\mathrm{OA}=7 \mathrm{cm}$, find the area of the shaded region. (Take $\pi =\frac{22}{7}$)

In Fig $13.96$, $\mathrm{PSR}$, $\mathrm{RTQ}$and $\mathrm{PAQ}$are three semicircles of diameter $10 \mathrm{cm}$,$3 \mathrm{cm}$ and $7 \mathrm{cm}$ respectively. Find the perimeter of shaded region.

In Fig., two circles with centres $\mathrm{A}$ and $\mathrm{B}$ touch each other at the point$\mathrm{C}$ . If $\mathrm{AC}=8 \mathrm{cm}$ and $\mathrm{AB}=3 \mathrm{cm}$, find the area of the shaded region.

In Fig., $\mathrm{ABCD}$is a square of side $2\mathrm{a}$, Find the ratio between the circumferences of internal circle to external circle

In the given figure, $\mathrm{ABCD}$ is a square of side $2a$. If the ratio between the areas of the incircle and the circumcircle of the square is $k:2$, then find the value of $k$.
      

In the following figure, there are three semicircles,$\text{A, B}$  and $\text{C}$ having diameter $3 \text{cm}$ each, and another semicircle $\text{E}$ having a circle $\text{D}$ with diameter$4.5 \text{cm}$  are shown. Calculate the cost of painting the shaded region at the rate of $25 \mathrm{paise}$ per ${\mathrm{cm}}^2$, to the nearest rupee. If the required answer is $₹ \mathrm{x}$, find the value of $x$.