Question

Find the radius of a circle whose area is equal to the sum of the areas of four other circles of radii 5m, 6m, 8m and 10m? ​

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \\ let \: the \: radius \: of \: circle \: whose \: area \\ is \: to \: be \: found \: be \: x.m \\ \\ similarly \\ let \: the \: radii \: of \: other \: four \: circles \: \\ be \: \: a.m \: , \: b.m \: , \: c.m \: and \: d.m \\ \\ so \: here \\ a = 5.m \\ b = 6.m \\ c = 8.m \\ d = 10.m$

$according \: to \: given \: condition \\ \\ \pi.x {}^{2} = \pi.a {}^{2} + \pi.b {}^{2} + \pi.c {}^{2} + \pi.d {}^{2} \\ \\ \pi.x {}^{2} = \pi(a {}^{2} + b {}^{2} + c {}^{2} + d {}^{2} ) \\ \\ = (5) {}^{2} + (6) {}^{2} +(8) {}^{2} + (10) {}^{2} \\ \\ = 25 + 36 + 64 + 100 \\ \\ x {}^{2} = 225$

$so \: thus \: then \\ \\ area \: of \: required \: circle = \\ \pi.x {}^{2} \\ \\ = 225\pi \: m {}^{2}$