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Sticky Note
The circumference of a circle is a? units and the area of the circle b? If a = b. What it the radius of the circle?
  1. 1
  2. 2
  3. 3
  4. None of these
Explanation

We are told:

  • Circumference of a circle = a

  • Area of the circle = b

  • And a = b

We know the formulas:

  • Circumference:

    a=2πra = 2pi r

  • Area:

    b=πr2r=0orr=

Since a=ba = b, set the formulas equal:

2πr=πr22pi r = pi r^2

Divide both sides by πpi:

2r=r22r = r^2

Rearrange:

r2−2r=0⇒r(r−2)=0r^2 - 2r = 0 Rightarrow r(r - 2) = 0

So the solutions are:

r=0 or r=2

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