SOLUTION: What is the diameter (in cm) of the circle whose area (in cm2) and circumference (in cm) have the same numerical value?
A. 1 cm B. 2 cm C. 3 cm D. π cm E. 4 cm
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Question 285533: What is the diameter (in cm) of the circle whose area (in cm2) and circumference (in cm) have the same numerical value?
A. 1 cm B. 2 cm C. 3 cm D. π cm E. 4 cm
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
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