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Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (use pi = 22/7)

Q (4)  Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm  (use \small \pi =\frac{22}{7} ) 

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Solution 

We know that 
l = r\Theta     ( where l is the length of the arc, r is the radius of the circle and \Theta is the angle subtended)

here    r = 100 cm 
   and  l = 22 cm 
Now,
               \Theta = \frac{l}{r} = \frac{22}{100}radian

We know that 
             \pi radian = 180\degree\\ \\So, 1radian = \frac{180}{\pi}degree\\ \\ \therefore \frac{22}{100}radian = \frac{180}{\pi}\times\frac{22}{100}degree\Rightarrow \frac{180\times7}{22}\times\frac{22}{100} = \frac{63}{5}degree \\ \\ So, \\ \\\frac{63}{5}degree = 12\frac{3}{5}degree = 12\degree + \frac{3\times60}{5}minute = 12\degree + 36'\\ \\ \therefore \frac{63}{5}degree = 12 \degree36' 
So, 
            Angle subtended at the centre of a circle       \Theta = 12\degree36'

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