question_answer

In the given figure, OACB is a quadrant of a circle with centre O and radius \[3.5\text{ }cm.\] If \[OD=2\text{ }cm\], find the area of the shaded region.

Answer:

Area of shaded region = Area of quadrant \[OACB-\]Area of \[\Delta \text{ }DOB\]

\[=\frac{90}{360}\times \pi \times {{(3.5)}^{2}}-\frac{1}{2}\times 2\times 3.5\]

\[=\frac{1}{4}\times \frac{22}{7}\times \frac{35}{10}\times \frac{35}{10}-3.5\]

\[=\frac{1925}{200}-3.5\]

\[=9.625-3.5=6.125\,\,c{{m}^{2}}\]

Hence, area of shaded region is \[6.125\text{ }c{{m}^{2}}\]