Question

Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.

Answer 1

Let the radius of the outer concentric circle be r.

Area enclosed between two concentric circles of radii 3.5 cm and 7 cm $=\pi (7^2-{3.5}^2)=\frac{22}{7}\times (7+3.5)\times (7-3.5)=115.5c{m}^2$

Now, according to the given information

$\pi (r^2-7^2)=\pi (7^2-{3.5}^{)}$

$\Rightarrow r^2-49=(7+3.5)(7-3.5)=10.5\times 3.5=36.75$

$\Rightarrow r^2=85.75$

$\therefore r=9.26cm$