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Question
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is ______.
Options
56 cm
42 cm
28 cm
16 cm
Solution
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is 28 cm.
Explanation:
Circumference of circle = Sum of circumference of two circles
`[("r"_1 = 36/2 = 18 "cm"),("r"_2 = 20/2 = 10 "cm")]`
⇒ 2πR = 2πr1 + 2πr2
2πR = 2π(r1 + r2)
⇒ R = r1 + r2 = 18 + 10
⇒ R = 28 cm.
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