Question 285533
Area = pi*r^2
Circumference = 2*pi*r


If area = circumference, then:


pi*r^2 = 2*pi*r


Divide both sides of this equation by pi to get:


r^2 = 2*r


Divide both sides of this equation by r to get:


r = 2


Diameter = 2*r so D = 4


Your answer is that the area and the circumference of a circle are equal when the diameter is equal to 4.


That would be selection E (4 cm).


Take half that diameter to get a radius of 2.


Circumference = 2*pi*r = 4*pi


Area = pi*r^2 = pi*2^2 = pi*4 = 4*pi


Area and Circumference are equal when the diameter is 4 cm.