Question

The radius of circle is $20$ cm The radii (in centimeters) of three concentric circle drawn in such a manner that the whole area is divided into four equal parts ,are

• A. $20\sqrt{2},20\sqrt{3},10$
• B. $\frac{10\sqrt{3}}{3},\frac{10\sqrt{2}}{3},\frac{10}{3}$
• C. $10\sqrt{3},10\sqrt{2},10$
• D. $17,14,10$

Answer 1

Answer: (C)

$10\sqrt{3},10\sqrt{2},10$

Suppose the radii of three circles are $r_1,r_2,r_3,$ where $r_1<r_2<r_3,$ then
$\pi r_1^2=\frac{1}{4}\pi {\left(20\right)}^2;\pi r_2^2=\frac{1}{2}\pi {\left(20\right)}^2;\pi r_3^2=\frac{3}{4}\pi {\left(20\right)}^2$
$\Rightarrow r_1^2:r_2^2:r_3^2:={10}^2:2\times {10}^2:3\times {10}^2$
$\Rightarrow r_1:r_2:r_3:=10:\sqrt{2}\times 10:\sqrt{3}\times :10$
$\therefore r_3:r_2:r_1:=10\sqrt{3}:10\sqrt{2}:10$