Question

The sum of the radii of two circles is 140cm and the difference of their circumferences is 88cm.
(i) Find the ratio between their areas. The side of a sq. is 20cm.
(ii) Find the areas of the circumscribed and inscribed circles.

• A. undefined
• B. undefined
• C. undefined
• D. undefined

Answer 1

(i) Let the radii be $r_1$ and $r_2$.
$r_1+r_2=140;2\pi (r_1-r_2)=88\Rightarrow (r_1-r_2)=14$
$\Rightarrow r_1-r_2=14$
Adding, $2r_1=154\Rightarrow r_1=77cm$
Also, $r_1-r_2=14\Rightarrow r_1=63cm$
Ration of areas $=\frac{\pi r_1^2}{\pi r_2^2}$ or $\frac{\pi r_2^2}{\pi r_1^2}$
$={\left(\frac{77}{63}\right)}^2$ or ${\left(\frac{63}{77}\right)}^2$
Ratio ${\left(\frac{121}{81}\right)}^2$ or ${\left(\frac{81}{121}\right)}^2$.

(ii)

$2r_1=\sqrt{(20{)}^2+(20{)}^2}\Rightarrow 2r_1=20\sqrt{2}\Rightarrow r_1=10\sqrt{2}cm\pi r_1^2=200\pi$

$2r_2=20\Rightarrow r_2=10cm\pi r_2^2=100\pi$
Hence, $Ratio=\frac{Areaofcircumscribed}{Areaofinscribed}=\frac{200\pi }{100\pi }=\frac{2}{1}\therefore 2:1$.