The radius of a metallic sphere is $9 \mathrm{cm}.$ It was melted to make a wire of diameter $4 \mathrm{mm}.$ Find the length of the wire.

In the figure, seg $\mathrm{AB}$ is a chord of a circle with centre $\mathrm{P}.$ If $\mathrm{PA}=8 \mathrm{cm}$ and distance of chord $\mathrm{AB}$ from the centre $\mathrm{P}$. is $4 \mathrm{cm},$ find the area of the shaded portion.

In the figure $7.48,$ square $\mathrm{ABCD}$ is inscribed in the sector $\mathrm{A}-\mathrm{PCQ}.$ The radius of sector $\mathrm{C}-\mathrm{BXD}$ is $20 \mathrm{cm}.$ Complete the following activity to find the area of shaded region.

In the figure $7.49,$ two circles with centres $\mathrm{O}$ and $\mathrm{P}$ are touching internally at point $\mathrm{A}.$ If $\mathrm{BQ}=9,\mathrm{DE}=5,$ complete the following activity to find the radii of the circles.