Question

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Answer 1

Answer:

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Answer 2

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Radius of one circle = 8cm
• Radius of another circle = 6cm

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The radius of the circle having area equal to the sum of the areas of the two circles

${\green{\underline{\underline{\bold{Solution:-}}}}}$

Radius of first circle = 8cm

Area of first circle = $π{r}^{2}$

= $π×{8}^{2} \\ \\</p><p></p><p>= 64π {cm}^{2}$

Radius of second circle = 6cm

Area of second circle = $π{r}^{2}$

= $π×{6}^{2} \\ \\</p><p></p><p>= 36π{cm}^{2}$

Sum of areas of two circles

= 64π + 36π

= 100π${cm}^{2}$

Radius =

$\sqrt {\frac{Area}{π}}\\ \\</p><p></p><p>= \sqrt {{100π}{π}} \\ \\</p><p></p><p>= \sqrt{100} \\ \\</p><p></p><p>= 10cm$

_______________

Formulas used :-

• Area of circle = $π{r}^{2}$

• Radius of circle = $\sqrt {\frac{Area}{π}}$