Question

Area of the shaded region in figure , if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOB =40° is *



(a)154/3 cm²

(b) 154 cm²

(c) 616 cm²

(d) 616/9 cm²​

Answer 1

Area of shaded region = ar (OAB) – ar (OCD)

$= \frac{\pi{r} {}^{2} 0}{36 {0}^{0} } - \frac{\pi{r} {}^{2}0 }{36 {0}^{0} }$

$= \frac{\pi0}{360 {}^{0} } ( {r}^{2} - {r}^{2} )$

$= \frac{22}{7} \times \frac{40 {}^{0} }{360 {}^{0} } (1 {4}^{2} - {7}^{2} )$

$= \frac{22}{7} \times \frac{1}{9} \times 12 \times 7$

$\huge \color{orange}{51.33c {m}^{2} }$