Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii \[15\] cm and \[18\] cm.

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Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii

$15$

cm and

$18$

cm.

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii

$15$

cm and

$18$

cm.

Given Radius of first circle =

${{r}_{1}}$

=

$15$

cm

Given Radius of second circle =

${{r}_{2}}$

=

$18$

cm

Therefore, Circumference of first circle of radius

${{r}_{1}}$

=

$2\pi {{r}_{1}}$

=

$30\pi$

cm

Circumference of second circle of radius

${{r}_{2}}$

=

$2\pi {{r}_{2}}$

=

$36\pi$

cm

Let us assume the radius of the circle = R

From the given question,

Circumference of circle = Circumference of first circle + Circumference of second circle

$2\pi R$

=

$2\pi {{r}_{1}}$

+

$2\pi {{r}_{2}}$

⇒

$2\pi R$

=

$30\pi$

+

$36\pi$

⇒

$66\pi$

⇒ R =

$33$

⇒ Radius =

$33$

cm

Therefore ,the required radius of a circle is

$33$

cm.

i

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