Question

The radius of a circle is $20cm$. If more concentric circles are drawn inside it in such a manner that it is divided into 4 equal parts, find the radius of the smallest circle.

• A. $5cm$
• B. $4cm$
• C. $10cm$
• D. $8cm$

Answer 1

The correct option is C $10cm$

Given: The radius of the circle $=20cm$
Area of circle $=\pi \times {20}^2=400\pi c{m}^2$
Now since the circle divides it into four parts of equal area.
Area of each shaded region $=\frac{1}{4}\times 400\pi =100\pi c{m}^2$
Area of largest circle drawn inside $=3\times 100\pi =300\pi c{m}^2$
Now let the radius of largest circle drawn inside be $r$.
$\Rightarrow \pi r^2=300\pi$
$\Rightarrow r^2=300$
$\Rightarrow r=\sqrt{300}=10\sqrt{3}cm$