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The radii of two circles are 19 cm and 9 cm respectively. Find

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The radii of two circles are $19 c m$ and $9 c m$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

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The radii of two circles are

19 c m

and

9 c m

respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

15 mins ago

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15 mins ago

Text solutionVerified

Let

r_{1}

and

C_{1}

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

r_{2}

and

C_{2}

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

Let

r_{3}

and

C_{3}

be the radius and circumference, respectively of the required circle.

r_{1} = 19

cm ...Given

Now

C_{1} = 2 π r_{1}

∴ C_{1} = 2 π \times 19 = 38 π

cm ...(1)

r_{2} = 9

cm ...Given

Now

C_{2} = 2 π r_{2}

∴ C_{2} = 2 π \times 9 = 18 π

cm ...(2)

C_{3} = C_{1} + C_{2}

....Given

∴ C_{3} = 38 π + 18 π

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

C_{3} = 56 π

cm.

2 π r_{3} = 56 π

∴ r_{3} = 28

The radius of the required circle is

28

cm.

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Question Text	The radii of two circles are $19 c m$ and $9 c m$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Answer Type	Text solution:1
Upvotes	150

The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Text solutionVerified

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The radii of two circles are $19 c m$ and $9 c m$ respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.