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Question

In Fig., $$OACB$$ is a quadrant of a circle with centre $$O$$ and radius $$3.5 cm$$. If $$OD = 2 cm$$, find the area of the
(i) quadrant $$OACB$$, (ii) Shaded region
465243.png


Solution

(i)
Area of quadrant $$OACB=\dfrac{\text{Area of Circle}}4 =\dfrac{\pi\times r^2}4 = \dfrac{1}{4}\times\dfrac{22}{7}\times3.5\times3.5$$ $$=9.625\,cm^2$$
(ii)
Area of the shaded region $$=$$ Area of Quadrant $$\,-\,$$Area of $$\triangle  BDO$$

$$=9.625-\left(\dfrac{1}{2}\times3.5\times2\right)$$

$$=\,6.125\,cm^2$$    

Mathematics
NCERT
Standard X

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