Question

Diameters of three concentric circles are in the ratio 1 : 2 : 3. The sum of the circumferences of these circles is 264 cm. Find the area enclosed between second and third circles.

Answer 1

$d_1=x,d_2=2x,d_3=3x$

Sum of circumference $=\pi (d_1+d_2+d_3)$

$\Rightarrow 264=\pi \left(6x\right)\Rightarrow x=14A_2=\pi r_2^2=\frac{\pi }{4}{d}_2^2=\frac{\pi }{4}\times 4x^2=196c{m}^2{A}_3=\frac{\pi d_3^2}{4}=\frac{\pi }{4}\times 9x^2=441\pi c{m}^2$