Question

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.​

Answer 1

Answer:

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Step-by-step explanation:

$so \: let \: the \: radii \: of \: two \: circles \: be \: \\ r1 \: \: and \: \: r2 \: \: respectively \\ \\ so \:here \\ r1 = 8.cm \\ r2 = 6.cm \\ \\ so \: area \: of \: circle \: with \: radius \: r1 \: is \\ \pi.r1 {}^{2} \\ = \pi.(8) {}^{2} \\ = 64.\pi \: \: \: \: \: \: \: (1)$

$similarly \: area \: of \: circle \: with \: radius \: r2 \\ = \pi.r2 {}^{2} \\ = \pi .(6) {}^{2} \\ = 36\pi \: \: \: \: \: \: (2)$

$so \: sum \: of \: areas \: of \: these \: circles \: is \\ 64.\pi + 36.\pi \\ = \pi(64 + 36) \\ = 100\pi \\ now \: use \: \pi = 3.14 \\ \\ = 3.14 \times 100 \\ = 314.cm {}^{2}$

$so \: hence \\ area \: of \: circle \: = \pi.r {}^{2} \\ = 314 = 3.14 \times r {}^{2} \\ r {}^{2} = 100 \\ \\ taking \: square \: roots \: on \: both \: sides \\ we \: get \\ r = 10 \: \: or \: \: r = - 10 \\ but \: as \: radius \: is \: never \: negative \: r = - 10 \: is \: absurd\\ r = 10.cm$

Answer 2

Answer:

Let the radius of required circle is r cm.

So, πr2

=πr12 +πr22

r2 =rr1+r 22

r 2 =(8) 2 +(6) 2

r 2=100

r=10cm

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