Question

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

Options

• 25 cm

• 31 cm

• 50 cm

• 62 cm

Answer 1

50 cm

Let r cm be the radius of the new circle.

Now,

Area of the new circle = Area of the circle with radius 24 cm + Area of the circle with radius 7 cm

Thus, we have:

`πr^2 = pi"r"_1^2 + pi"r"_2^2`

`=> pi"r"^2=[pixx(24)^2+pixx(7)^2]"cm"^2`

`=>pi"r"^2 = [pixx576+pixx49]"cm"^2`

`=>pi"r"^2 = pixx(576+49) "cm"^2`

`=> "r"^2 = 625  pi  "cm"^2`

`=>"r"^2 = 625`

`=> "r" = 25`

∴ Diameter of the new circle = (25 × 2) cm

                                               = 50 cm