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? - IQ786

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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?

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

2

3

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:
$a = 2pi r$
Area:
$b = π r^{2}$

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

$2pi r = pi r^2$

Divide both sides by $pi$ :

$2r = r^2$

Rearrange:

$r^2 - 2r = 0 Rightarrow r(r - 2) = 0$

So the solutions are:

r=0 or r=2