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

Algebra ->  Circles -> 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      Log On


   

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) About Me  (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.