Question

Two radii OA and OB form an angle of ${60}^o$ for two concentric circles with $8$ and $5$ cm radii. Calculate the area of the circular trapezoid formed by the radii and concentric circles.

• A. $18.73c{m}^2$
• B. $15.36c{m}^2$
• C. $32.73c{m}^2$
• D. $20.42c{m}^2$

Answer 1

The correct option is D $20.42c{m}^2$

Let $r_1=8cm,r_2=5cm,\theta ={60}^{\circ }=\frac{\pi }{3}$

Area of sector is given by $\frac{1}{2}{r}^2\theta$

A1 = Area of bigger sector = $\frac{64}{2}\times \frac{\pi }{3}=\frac{32\pi }{3}$

A2 = Area of smaller sector = $\frac{25}{2}\times \frac{\pi }{3}=\frac{25\pi }{6}$

Area of trapezoid $=A1–A2$

$=\frac{32\pi }{3}-\frac{25\pi }{6}=\frac{13\pi }{2}=20.4c{m}^2$