Question

The number of square inches of a circled area is equal to the number of inches of its circumference. What is the radius of the circle?

Answer 1

`r = 2`

Explanation:

The area of a circle is related to the radius:

`A = \pi r^2`

and the circumference is related to the radius:

`p = 2 \pi r`

we know that (ignoring units) the number resulting for both of these is the same, i.e.

`\pi r^2 = 2 \pi r`

we can divide both sides by `\pi r` to get

`r = 2`

Answer 2

`"radius "=2`

Explanation:

`"equate area of circle to circumference of circle"`

`rArrpir^2=2pirlarr"divide both sides by "pi`

`rArrr^2=2r`

`rArrr^2-2r=0larr" common factor of r"`

`rArrr(r-2)=0`

`rArrr=0" or "r=2`

`r>0rArrr=2`