OACB is a quadrant of a circle with centre O and its radius is 3.5 cm.

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.

 

Solution:

(i) Area of the quadrant $O A C B=\left(\frac{1}{4} \times \frac{22}{7} \times 3.5 \times 3.5\right) \mathrm{cm}^{2}$

$=\left(\frac{1}{4} \times \frac{22}{7} \times \frac{35}{10} \times \frac{35}{10}\right) \mathrm{cm}^{2}$

$=\frac{77}{8} \mathrm{~cm}^{2}$

$=9.625 \mathrm{~cm}^{2}$

(ii) Area of the shaded region = Area of the quadrant $O A C B$ - Area of $\triangle A O D$

$=\left|\left(\frac{77}{8}\right)-\left(\frac{1}{2} \times 3.5 \times 2\right)\right| \mathrm{cm}^{2}$

$=\left(\frac{77}{8}-\frac{35}{10}\right) \mathrm{cm}^{2}$

$=\frac{49}{8} \mathrm{~cm}^{2}$

$=6.125 \mathrm{~cm}^{2}$

 

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