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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.
Areas Related to Circles | Exercise 11.3 | Maths | NCERT Exemplar
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.

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