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Question
Find the area of the circle, length of whose circumference is equal to the sum of the lengths of the circumferences with radii 15 cm and 13 cm.
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Solution
In a circle
Circumference = Sum of circumferences of two circle of radii 15 cm and 13 cm
Now circumference of first smaller circle = 2πr
= `2 xx 22/7 xx 15 = 660/7` cm
Circumference of the second smaller circle
= `2 xx 22/7 xx 13 = 572/7` cm
∴ Circumference of the bigger circle
= `660/7 + 572/7 = 1232/7` cm
Let R be its radius, then
`2pi"R" = 1232/7 ⇒ (2 xx 22)/7 "R" = 1232/7`
⇒ R = `1232/7 xx 7/44 = 28` cm
∴ Area of the circle = `pi"R"^2`
= `22/7 xx 28 xx 28 "cm"^2 = 2464` cm2
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