Question

In the given figure, the area of the shaded portion is 770 cm². If the circumference of the outer circle is 132 cm, find the width of the shaded portion.

Answer 1

From the given data, we can calculate the area of the outer circle and then the area of the inner circle and hence the width of the shaded portion.

Given that the circumference of the outer circle is 132 cm

Thus, we have, 2πR = 132 cm

⇒ R = `[ 132 xx 7 ]/[ 2 xx 22 ]`

⇒ R = 21 cm

Area of the bigger circle = πR²

= `22/7` × 21²

= 1386 cm²

Also given the area of the shaded portion.

Thus, the area of the inner circle = Area of the outer circle - Area of the shaded portion

= 1386 - 770

= 616 cm²

⇒  πr² = 616

⇒ r² = `[ 616 xx 7 ]/22`

⇒ r² = 196

⇒ r = 14 cm

Thus, the width of the shaded portion = 21 - 14 = 7 cm.