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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.
Solution
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
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