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.

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Answer 1

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Answer 2

$\huge\underline \mathbb {SOLUTION:-}$

Answer:

• Radius of the circle = 10 Cm.

Given:

• Radius of the first circle is 8 Cm.
• Radius of the second circle is 6 cm.

Need To Find:

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

Explanation:

Radius of 1st circle = 8cm (Given)

$\therefore$Area of 1st circle = π(8)² = 64π

Radius of 2nd circle = 6cm (Given)

$\therefore$Area of 2nd circle = π(6)² = 36π

$\underline \mathsf \red {So\: :-}$

The sum of 1st and 2nd circle will be = 64π + 36π = 100π

$\underline \mathsf \blue {Now\: :-}$

Assume that the radius of 3rd circle = R

$\therefore$Area of 3rd circle = πR²

It is given that:

The area of the 3rd circle = Area of 1st circle + Area of 2nd circle

$\underline \mathsf \pink {Or\: :-}$

$:\implies$πR² = 100π Cm²

$:\implies$R² = 100 Cm²

$\underline\mathsf \green {Therefore \: :-}$

$:\implies$Radius = 10 Cm.

• Hence, the radius of the circle = 10 Cm.

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