Question

area of circle is equal to the sum of the area of two circles of diameter 40 cm 9 cm. find the diameter of new circle.

Answer 1

$let \: the \: radius \: of \: the \: new \: cirle = r \\ \\ given \: that \: diameter \: of \: a \: circle = 40 \\ \\ therefore \: radius \: = \frac{40}{2} = 20 \: cm \\ \\ area \: of \: this \: cirle = \pi \times 20 {}^{2} \\ \\ = 400\pi\\ \\ and \: given \: that \: diameter \: of \: another \: circle = 9 \: cm \\ \\ therefore \: radius = \frac{9}{2} cm \\ area \: of \: this \: circle = \pi \times (\frac{9}{2} ) {}^{2} \\ \\ = \frac{81}{4} \pi \\ \\now \: area \: of \: the \: new \: circle = \pi \times r {}^{2} \\ \\ therefore \: according \: to \: question \\ \\ \pi \times r {}^{2} = 400\pi + \frac{81}{4} \pi \\ \\ = > \pi \times r {}^{2} = \frac{1681}{4} \pi \\ \\ = > r {}^{2} = \frac{1681\pi}{4\pi} \\ \\ = > r {}^{2} = \frac{1681}{4} \\ \\ = > r = \sqrt{ \frac{1681}{4} } \\ \\ = > r = \frac{41}{2} cm\\ \\ therefore \: diameter = 2 \times r \\ \\ = \frac{41}{2} \times 2 \\ \\ = 41 \: cm$


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Answer 2

Answer:

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