SOLUTION: 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 (A) 31 cm (B) 25 cm (C) 62 cm (D) 50 cm

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Question 239338: 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
(A) 31 cm (B) 25 cm (C) 62 cm (D) 50 cm
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
area of a circle equals pi*r^2

radius of your two smaller circles are:

24 cm and 7 cm

area of your two smaller circles are:

pi*24^2 + pi*7^2

Sum of these areas is equal to:

pi*(24^2 + 7^2) = pi * (576 + 49) = pi * (625)

pi*625 is the area of your new circle that is equal to the sum of the areas of the two smaller circles.

Since pi*625 is equal to pi*r^2, this means that r^2 = 625 which means that r = sqrt(625) = 25.

Since the radius of your new circle equals 25, the diameter must be equal to 2*25 = 50.

That would be selection D.