<PRE><B>Question 239338</B>
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.


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