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 __________.

Answer 1

Let the radius of the circle be r cm.

Suppose the radii of two given circles be r₁ cm and r₂ cm.

Diameter of the first circle = 36 cm

⇒ 2r₁ = 36 .....(1)

Diameter of the second circle = 20 cm

⇒ 2r₂ = 20 .....(2)

Now,

Circumference of the circle = Circumference of the first circle + Circumference of the second circle

$$\begin{gathered} \Rightarrow 2\mathrm{\pi }r=2\mathrm{\pi }{r}_1+2\mathrm{\pi }{r}_2 \\ \Rightarrow 2r=2r_1+2r_2 \\ \Rightarrow 2r=36+20=56\left[\mathrm{From}\left(1\right)\mathrm{and}\left(2\right)\right] \\ \Rightarrow r=\frac{56}{2}=28\mathrm{cm} \end{gathered}$$

Thus, the radius of the circle is 28 cm.

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___.