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  • 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.

2. 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.

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We know that the area of the circle is   :    =\ \pi r^2

Thus area of a 1st circle  :    =\ \pi r^2_1

or                                       =\ \pi \times 8^2\ =\ 64 \pi\ cm^2

And the area of a 2nd circle is   :  =\ \pi r^2_2

or                                         =\ \pi \times 6^2\ =\ 36\pi\ cm^2

According to the question area of the new circle is   =\ 64\pi\ +\ 36\pi\ =\ 100\pi\ cm^2

or                                           \pi r^2\ =\ 100 \pi

or                                              r\ =\ 10\ cm

Hence the area of the new circle is 10 cm.

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Devendra Khairwa

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