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The radii of two circles are 8 cm and 6 cm respectively. Find

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

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The radii of two circles are

8 c m

and

6 c m

respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Let

r_{1}

and

A_{1}

be the radius and area, respectively of 1st circle and

r_{2}

and

A_{2}

be the radius and area, respectively of 2nd circle.

Let

r_{3}

and

A_{3}

be the radius and area, respectively of required circle.

r_{1} = 8

cm ...Given

A_{1} = π r_{1}^{2}

∴ A_{1} = π \times 8^{2} = 64 π c m^{2}

...(1)

r_{2} = 6

cm ...Given

A_{2} = π r_{2}^{2}

∴ A_{2} = π \times 6^{2} = 36 π c m^{2}

...(2)

A_{3} = A_{1} + A_{2}

....Given

∴ A_{3} = 64 π + 36 π

....From (1) and (2)

A_{3} = 100 π c m^{2}

π r_{3}^{2} = 100 π

r_{3} = 10

The radius of the required circle is

10

cm.

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Question Text	The radii of two circles are $8 c m$ and $6 c m$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles
Answer Type	Text solution:1
Upvotes	154

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

Text solutionVerified

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