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 so that the area enclosed between it and the 7 cm circle is same as that between two inner circle. find the radius of third circle.

Answer 1

Hence, radius of 3rd circle is 9.26cm

Answer 2

Answer:

9.26 cm

Step-by-step explanation:

Let the radius of inner circle be $r_1$

Let the radius of outer circle be $r_2$

Let the radius of the outermost circle be $r_3$

Now we are given that 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 so that the area enclosed between it and the 7 cm circle is same as that between two inner circle

SO, $A_1=A_2$

$\pi (r_2)^2-\pi (r_1)^2 = \pi (r_3)^2-\pi(r_2)^2$

$(r_2)^2- (r_1)^2 = (r_3)^2-(r_2)^2$

$2(r_2)^2- (r_1)^2 = (r_3)^2$

$2(7)^2- (3.5)^2 = (r_3)^2$

$\sqrt{2(7)^2- (3.5)^2} = (r_3)$

$9.26 = (r_3)$

Hence the radius of third circle is 9.26 cm