The Circumference of a circle is equal to the area of the circle. Find the radius.
Thanks.
Circumference = 2 times pi times r
Area = pi times r-squared
If Area = Circumference, then..
(2)(pi)(r) = (pi)(r^2)
Divide both sides by r
2(pi) = (pi)(r)
Now, solve for r by dividing both sides by pi.
Thanks!
To find the radius of a circle when the circumference is equal to the area, we can use the formulas for the circumference and area of a circle.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
The formula for the area of a circle is A = πr², where A represents the area and r represents the radius.
In this case, we are given that the circumference (C) is equal to the area (A), so we can set up the equation as follows:
2πr = πr²
To solve for the radius (r), we can simplify the equation by dividing both sides by π:
2r = r²
Now, we can rearrange the equation to bring all terms to one side:
r² - 2r = 0
Next, we can factor the equation:
r(r - 2) = 0
Setting each factor equal to zero, we get two possible solutions:
r = 0 or r - 2 = 0
Since a circle cannot have a radius of zero, we discard that solution. Therefore, the only valid solution is:
r - 2 = 0
Adding 2 to both sides of the equation, we find:
r = 2
Therefore, the radius of the circle is 2.
Note: It is also possible to solve this equation algebraically by squaring both sides of the equation 2πr = πr² and simplifying. However, since the equation is quadratic, factoring is a quicker and simpler method.