Question

What is the diameter of a circle whose area is equal to the sum of the areas of two corcles of radii 40cm and 9cm?

Answer 1

Let r​1=radius of first circle=40cm.

Let r2=radius of second circle=9cm.

area of first circle = π r1^2

=π(40)2 = 1600π cm^2

area of second circle = π r2^2

= π(9)2 = 81π cm^2

area of required circle = area of first circle + area of second circle

= 1600π + 81π

= 1681π cm^2

Let R = radius of required circle

So, πR^2 = 1681π

⇒ R^2 = 1681

⇒ R = √1681

= 41 cm

So, diameter of required circle = 2R = 2 × 41 =82 cm

Hence diameter of the circle=82cm