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The radii of two circles are 48 cm and 13 cm. Find the area of the circle which has its circumference equal to the difference of the circumferences of the given two circles.

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#### Solution

Circumference of the first circle

s_{1} = 2π x 48

= 96πcm

Circumference of the first circle

s_{2} = 2π x 13

= 26πcm

Let r be the radius of the resulting circle.

2πr = 96π - 26π

2πr = 70π

r = `(70π)/(2π)`

= 35cm

Hence area of the circle

A = πr^{2 }

= π x 35^{2}

= 3850cm^{2 }

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