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The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle. - Mathematics

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Sum

The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.

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Solution

Let the radius of the circle be r cm. Then, Diameter = 2r cm and Circumference = 2πr cm

It is given that the circumference exceeds the diameter by 16.8 cm

∴ Circumference = Diameter + 16.8

⇒ 2πr = 2r + 16.8

`⇒ 2 × \frac { 22 }{ 7 } × r = 2r + 16.8`

⇒ 44r = 14r + 16.8 × 7

⇒ 44r – 14r = 117.6 ⇒30 r = 117.6

`⇒ r = \frac { 117.6 }{ 30 } = 3.92`

Hence, radius = 3.92 cm

Concept: Circumference of a Circle
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