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

The area enclosed between the two circles of radii 3.5 cm and 7 cm 

`= pi(7^2-3.5^2)` 

`= 115.5 cm^2`

Let the radius of the outermost circle be r cm.
Area betweent the circles with radius r and 7 cm=Area between the circles with radius 7 cm and 3.5 cm 

`pi(r^2-7^2)=115.5`

`⇒ (r^2-7^2)=115.5/pi`

`⇒ r^2=36.75+49=85.75 cm^2`

`⇒ r=9.26 cm`