Question

The shaded portion of the figure, given alongside, shows two concentric circles. If the circumference of the two circles is 396 cm and 374 cm, find the area of the shaded portion.

Answer 1

Let R and r be the radius of the big and small circles respectively.
Given that the circumference of the bigger circle is 396 cm

Thus, we have,
2πR = 396 cm

⇒ R = `[ 396 xx 7 ]/[ 2 xx 22 ]`

⇒ R = 63 cm

Thus, the area of the bigger circle = πR²
= `22/7 xx 63^2`

= 12474 cm²

Also, given that the circumference of the smaller circle is 374 cm
⇒ 2πr = 374

⇒ r = `[ 374 xx 7 ]/[ 2 xx 22 ]`
⇒ r = 59.5 cm

Thus, the area of the smaller circle = πr²
= `22/7` x 59.5²

= 11126.5 cm²
Thus the area of the shaded portion = 12474 - 11126.5 = 1347.5 cm²