Question

An archery target has three regions formed by three concentric circles as shown in the given figure. If the diameters of the circles are in ratio 1:2:3, then find the ratio of the areas of three regions.​

Answer 1

$\red{\bf {Solution}}$

The diameter of three concentric circles are in the ratio of $\tt\color{orchid}{1 : 2 : 3}$

Let the diameter of the three circles be$\tt\color{red}{1\: cm, \:2 \:cm \:and \:3\: cm\: respectively.}$

$\bold{So,}$

Their radii will also be in the ratio of$\tt\color{blue}{1 : 2 : 3.}$

$\bold{Therefore,,}$

$\small\textbf{the radii of three concentric circle will be}$

$\sf\color{teal}{1/2 cm \:, 2/2 cm}$

$\underline{\boxed{\sf\purple{= 1 \:cm\: and \:3/2\: cm}}}$

$\textbf\color{orange}{Ratio of their areas}$

$\underline{\boxed{\sf\purple{= πr₁² : πr₂² : πr₃²}}}$

$\bold{= 22/7*1/2*1/2 : 22/7*1*1 : 22/7*3/2*3/2}$

$\green{\bf {= 1/4 : 1 : 9/4}}$

Thankyou :)