Question

The area enclosed between two concentric circles is 770 cm². If the radius of the outer circle is 21 cm, find the radius of the inner circle.

Answer 1

Given: Let the radius of the inner circle = r

Area enclosed between two concentric circles = 770cm²

and Radius of the outer circle, R = 21cm

∴ The area enclosed between two concentric circles

= Area of the Outer circle – Area of the inner circle

770 = πR² – πr²

770 = π(21² – r²)

245 = 441 – r²

⇒ r² = 441 – 245

⇒ r² = 196

⇒ r = √196

⇒ r = ±14

⇒ r = 14cm [taking positive square root, because radius can’t be negative]

Hence, the radius of the inner circle is 14cm.