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

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Solution

Let r be the radius of the circle whose area is equal to the sum of the areas of circles of radii 8 cm and 6 cm. Then,

$π r^{2} = π \times 8^{2} + π \times 6^{2}$

$\Rightarrow r^{2} = 100$

$\Rightarrow r = 10 c m$

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

Let r be the radius of the circle whose area is equal to the sum of the areas of circles of radii 8 cm and 6 cm. Then, πr2=π×82+π×62 ⇒r2=100 ⇒r=10 cm

Let r be the radius of the circle whose area is equal to the sum of the areas of circles of radii 8 cm and 6 cm. Then,

$π r^{2} = π \times 8^{2} + π \times 6^{2}$

$\Rightarrow r^{2} = 100$

$\Rightarrow r = 10 c m$