Two circles are concentric with circumference 154 cm and 88 cm respectively.  Find the area of ring?

1270.5

OP = r₂ , OQ = r₁

Area of ring = πr₂² - πr₁²

circumference of circle (OP) = 2πr₂ = 154

⇒ r₂ = \(\frac{154 × 7}{22 × 2}\) = \(\frac{49}{2}\) = 24.5

Circumference of circle OQ = 2πr₁ = 88

⇒ r₁ = \(\frac{88 × 7 }{22 × 2}\) = 14

Area of ring = πr₂² - πr₁²

                   = π(r₁+r₂) (r₂ -r₁)

                  = π (10.5) (38.5) = 1270.5 cm²