Challenging Circles

Geometry Level 2

In a circle of radius r r cm, an arc of length l l cm subtends angle θ \theta at the centre of the circle and the region bounded by the arc and the radius has area A A c m 2 { cm }^{ 2 } .

when r > x r>x then A > l A>l

but,if r < x r<x then A < l A<l

where x x is an integer.

Find the value of x


The answer is 2.

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Inderjeet Nair by Inderjeet Nair , 22, India

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1 solution

Inderjeet Nair
Jan 18, 2015

Now let us find the relationship between A and l A = θ 360 Π r 2 A = θ 360 Π r × r A = ( θ 360 2 Π r ) × 1 2 r A = r 2 l A=\frac { \theta }{ 360 } \Pi { r }^{ 2 }\\ A=\frac { \theta }{ 360 } \Pi r\times r\\ A=(\frac { \theta }{ 360 } 2\Pi r)\times \frac { 1 }{ 2 } r\\ A=\frac { r }{ 2 } l

thus the value of x is 2 i.e. if the value of r is greater than 2 then A>l but if value of r is smaller than 2 then A<l

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