Question

The area of a circular ring enclosed between two concentric circles is 88 cm 2. Find the radii of the two circles, if their difference is 1 cm.

Answer 1

Let r cm be the radius of inner circle. 

Radius of outer circle = (r+ 1) cm 

Area of circular ring = Area of outer cirde - area of inner circle 

⇒  π (r + 1)² - π r¹ = 88 

⇒ π (r¹ + 2r + 1) - π r² = 88 

⇒ π r¹ + 2 π r + π - πr¹ = 88 

⇒ `22/7 (2"r" + 1) = 88`

⇒ 2r + 1 = `88 xx 7/22` 

⇒ 2r + 1 = 28

⇒ 2r = 27

⇒ r = `27/2 = 13.5` cm

(r + 1) = 13.5 + 1 = 14.5 cm

Therefore, radii are 13.5 cm and 14.5 cm.