Question

The area enclosed between between the circumferences of two concentric circles is 2464 sq cm. If their radii are in the ratio 5:3 calculate:
A) the area of outer circle
B) the circumference of the inner circle.
If a third circle is drawn, outside the larger circle, so that the area enclosed between this circle is twice the area enclosd between the given circles, claculate the area of the circles.

Answer 1

$\pi (r_2^2-r_1^2)=2464c{m}^2\frac{r_2}{r_1}=\frac{5}{3}\Rightarrow r_2=\frac{5}{3}{r}_1\therefore \pi [\frac{25}{9}{r}_1^2-r_1^2]=2464\Rightarrow r_1^2=\frac{2464\times 7\times 9}{16\times 22}\Rightarrow r_1^2=\frac{784\times 9}{16}\Rightarrow r_1=\frac{28\times 3}{4}\Rightarrow r_1=21cm.r_2=\frac{5}{3}\left(21\right)\Rightarrow r_2=35cm$.
$\therefore$ (A) Area of outer circle $=\pi r_2^2=\frac{22}{7}(35{)}^2$
$=3850c{m}^2$
(B) Circumference of inner circle $=2\pi r_1=2\pi \left(21\right)$
$=132cm$.
Third circle $=2\times \left(shadedarea\right)=2\times \left(2464\right)=4928c{m}^2$
Area of inner circle $=1386c{m}^2$
Area of outer circle $=3850c{m}^2$
Area of third circle $=4928c{m}^2$