Question

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is ______.

Options

• 31 cm

• 25 cm

• 62 cm

• 50 cm

Answer 1

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm.

Explanation:

Let, r₁ = 24 cm

r₂ = 7 cm

Area of first circle = `pir_1^2`

= `pi(24)^2`

= `576 pi  cm^2`

Area of second circle = `pir_2^2`

= `pi(7)^2`

= `49 pi  cm^2`

We have, 

Area of circle = Area of first circle + Area of second circle

`piR^2 = 576pi + 49pi`

R = 25 cm

Required diameter of circle = `2 xx 25`

= 50 cm