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

Answer 1

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.