Mathematics
In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.
![In the figure, the area enclosed between the circumferences of two concentric circles is 346.5 cm^2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q11b-c16-ex-16-3-mensuration-ml-aggarwal-solutions-icse-class-9-758x756.png)
Mensuration
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Answer
Let radius of inner circle = r cm.
Circumference = 2πr
⇒ 88 = 2πr
⇒ r =
⇒ r =
⇒ r =
⇒ r = 2 × 7 = 14 cm.
Let radius of outer circle = R cm.
From figure,
Area of shaded region = Area of outer circle - Area of inner circle
⇒ 346.5 = π(R)2 - πr2
⇒ 346.5 = π(R)2 - π(14)2
⇒ 346.5 = π(R2 - 196)
⇒ R2 - 196 =
⇒ R2 - 196 =
⇒ R2 - 196 =
⇒ R2 - 196 = 110.25
⇒ R2 = 110.25 + 196
⇒ R2 = 306.25
⇒ R =
⇒ R = 17.5 cm
Hence, radius of outer circle = 17.5 cm.
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