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 ______.

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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 = $\frac{36}{2}$ = 18 "cm"),("r"_2 = $\frac{20}{2}$ = 10 "cm")]` $\Rightarrow$ 2$\pi$R = 2$\pi$r1 + 2$\pi$r2 2$\pi$R = 2$\pi$(r1 + r2) $\Rightarrow$ R = r1 + r2 = 18 + 10 $\Rightarrow$ R = 28 cm.

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