Question

OACB is a quadrant of a circle with centre O and its radius is 3.5 cm. If OD = 2 cm. find the area of (i) quadrant OACB (ii) the shaded region.

Answer 1

(i) Area of the quadrant OACB $=\left(\frac{1}{4}\times \frac{22}{7}\times 3.5\times 3.5\right){\mathrm{cm}}^2$
$$\begin{gathered} =\left(\frac{1}{4}\times \frac{22}{7}\times \frac{35}{10}\times \frac{35}{10}\right){\mathrm{cm}}^2 \\ =\frac{77}{8}{\mathrm{cm}}^2 \\ =9.625{\mathrm{cm}}^2 \end{gathered}$$

(ii) Area of the shaded region = Area of the quadrant OACB $-$ Area of $∆AOD$
$$\begin{gathered} =\left|\left(\frac{77}{8}\right)-\left(\frac{1}{2}\times 3.5\times 2\right)\right|{\mathrm{cm}}^2 \\ =\left(\frac{77}{8}-\frac{35}{10}\right){\mathrm{cm}}^2 \\ =\frac{49}{8}{\mathrm{cm}}^2 \\ =6.125{\mathrm{cm}}^2 \end{gathered}$$