Question

the circumference of a circle exceeds its diameter by 30 centimetres. find the radius of the circle.

Answer 1

Heya

let the radius of the circle be r cm Then ,

Diameter , D = 2r Cm

and Circumference = 2 πr Cm

it is given that the circumference exceeds the diameter by 30 cm that is

circumference = Diameter + 30 cm

2 πr = 2 ( r + 15 ) cm

$\frac{22}{7} \times r \: = r \: + 15 \\ \\ = 22r \: = 7r \: + 105 \\ \\ = 22r - 7r \: = 105 \\ \\ = 15r \: = 105 \\ \\ = r \: = \frac{105}{15} \\ \\ = r \: = 7 \: cm$
Hence the radius of the circle is 7 cm

Thanks !!

Answer 2

Heya!
Here's your answer!
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As we know ,
Formula for circumference of a circle = 2πr

Since 2r = Diameter

We may also write this formula as ,
= πd (d represents diameter)

Now ,
As mentioned in the question ,
Circumference - diameter = 30 cm

We'll calculate ,

=> 2πr - d = 30

=> πd - d = 30

=> d ( π - 1 ) = 30

=> d ( 22/7 - 1 ) = 30

=> d x 15/7 = 30

=> d = 30 x 7/15

=> d = 14 cm

Therefore ,
Radius = diameter / 2 = 7 cm

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Hope this helps! ^^