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
Area of first circle = πr2 = π(24)2 = 576π m2
Area of second circle = πr2 = π(7)2 = 49π m2
Now, we are given that,
Area of the circle = Area of first circle + Area of second circle
∴ πR2 = 576π +49π
(where, R is the radius of the new circle)
⇒ πR2 = 625π
⇒ R2 = 625
⇒ R = 25
∴ Radius of the circle = 25cm
Thus, diameter of the circle = 2R = 50 cm.