Question

The radii of the two circles are 19 cm and 9 cm respectively. The radius of the circle which has a circumference equal to the sum of the circumference of two circles is ____________.

Options

• 35 cm

• 10 cm

• 21 cm

• 28 cm

Answer 1

The radii of the two circles are 19 cm and 9 cm respectively. The radius of the circle which has a circumference equal to the sum of the circumference of two circles is 28 cm.

Explanation:

Let the radii of two circles are r₁ and r₂ and the radius of the large circle be r.

`therefore "r"_1 = 19  "cm", "r"_2 = 9  "cm"`

Circumference of two circles = C₁+ C₂ …(where C = circle)

`= 2 pi "r"_1 + 2 pi "r"_2`

`= 2 pi xx 19 + 2 pi xx 9`

`= 38 pi + 18 pi`

`= 56 pi`

`therefore  "Circumference of large circle" = 56 pi`

`=> 2 pi "r" = 56 pi`

`=> "r" = 28`

`therefore "Radius of large circle" = 28  "cm"`