# Area 6

### From Homeworkwiki

**Problem: The area of the ring between two concentric circles is 1694 sq. cm.**

**If the width of the ring is 7 cm, find the radii of the circles.**

**Solution:** Let the radius of the inner circle be x cm

Radius of the outer circle is (x + 7)cm

Area of the ring = Π[(x + 7)^{2} - x^{2}] cm^{2}

= Π(2x + 7)(7) cm^{2}

∴ Π(2x + 7)(7) = 1694

2x + 7 = 1694 × 7/22 × 1/7 = 77

2x + 7 = 77

2x = 77 – 7

2x = 70

⇒ x = 70/2 = 35

∴ Radius of the inner circle is 35 cm and that of the outer circle is 35 + 7 = 42 cm.