Question

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

• A. $20\sqrt{2},20\sqrt{3},20$
• 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, 9

Answer 1

The correct option is C $10\sqrt{3},10\sqrt{2},10$

OA is the radius of the largest circle and O is the centroid of the all concentric circles.
Let $r_1,r_2,r_{3}and{r}_4$ be the radii of the concentric circles in increasing order then
Total area of given circle
$=\pi \times (20{)}^2=400\pi$
Area of each region $=\frac{1}{4}\times 400\pi =100\pi$
$\therefore$ Area of central region $=100\pi =\pi r_1^2$
$\Rightarrow$ $r_1$ = 10 cm
Similarly, area of second region $=100\pi =\pi (r_2^2-r_1^2)$
$=100\pi =\pi (r_2^2-100)$
$\Rightarrow r_2=10\sqrt{2}cm$
Again, area of third region $=100\pi =\pi (r_3^2-r_2^2)$
$100\pi =\pi (r_3^2-200)$
$\Rightarrow$ $r_3^2=10\sqrt{3}cm$
$\therefore$ The required radii are 10, $10\sqrt{2}and10\sqrt{3}$