Question

If the circumference is 21+2.5pi what is the area

Answer 1

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Circumference = 21 + 2.5 π

Or, 2×π×r = 21 + 2.5 π

$or, \: \pi \times r = \frac{21 + 2.5 π}{2}$

$or, \: \pi \times r = \frac{21}{2} + \frac{25\pi}{2}$

$or, \: r \: = ( \frac{21}{2} + \frac{25\pi}{2} ) \div \frac{22}{7}$

$or, \: r = (\frac{7}{22} \times \frac{21}{2} ) + ( \frac{7}{22} \times \frac{2.5\pi}{2} )$

$or, \: r = (\frac{7}{22} \times \frac{21}{2} ) + ( \frac{7}{22} \times \frac{2.5}{2} \times \frac{22}{7} )$

$or, \: r = (\frac{7}{22} \times \frac{21}{2} ) + ( \frac{2.5}{2} )$

$or, \: r = ( \frac{147}{44} ) + ( \frac{55}{44} )$

$or, \: r = ( \frac{101}{22} )$

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Now, area of the circle

= π r²

$= \frac{22}{7} \times \ { \frac{101}{22} }^{2}$

$= \frac{22}{7} \times \ { \frac{101}{22} } \times \frac{101}{22}$

$= { \frac{101}{7} } \times \frac{101}{22}$

$= \frac{10201}{154}$

$= 66.24$

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