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Question
The diameter of two circles are 28 cm and 24 cm. Find the circumference of the circle having its area equal to sum of the areas of the two circles.
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Solution
Let R be the radius of the big circle.
The radii of two circles are
r1 = `"d"_1/(2) = (28)/(2) = 14"cm"`
and
r2 = `"d"_2/(2) = (24)/(2) = 12"cm"`
Now,
Area of big circle
= Sum of areas of circles of radii r1 and r2
⇒ πR2 = πr12 + πr22
⇒ R2 = r12 + r22
⇒ R2 = 142 + 122
⇒ R2 = 196 + 144
⇒ R2 = 340
⇒ R = 18.4
∴ Circumference of big circle
= 2πR
= `2 xx (22)/(7) xx 18.4`
= 115.65cm2.
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