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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.
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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