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In the figure (i) given below, the area enclosed between the concentric circles is 770 cm2. Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

In the figure, the area enclosed between the concentric circles is 770 cm^2. Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Mensuration

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Answer

Let radius of inner circle = r cm.

From figure,

Area of shaded region = Area of outer circle - Area of inner circle

⇒ 770 = π(21)2 - πr2

⇒ 770 = 441π - πr2

⇒ 770 = π(441 - r2)

⇒ 441 - r2 = 770π\dfrac{770}{π}

⇒ 441 - r2 = 770227\dfrac{770}{\dfrac{22}{7}}

⇒ 441 - r2 = 770×722\dfrac{770 \times 7}{22}

⇒ 441 - r2 = 245

⇒ r2 = 441 - 245

⇒ r2 = 196

⇒ r = 196\sqrt{196} = 14 cm.

Hence, radius of inner circle = 14 cm.

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