If the number of units in the circumference of a circle is the same as the number of square units in its area, then the diameter of the circle is
(A) 2
(B) π
(C) 4
(D) 2Ï€
(E) π^2
I'm confused between A and C. Can any experts help?
Hi ardz24,
Let's take a look at your question.
The questions states:
"the number of units in the circumference of a circle is the same as the number of square units in its area", which can be written as:
Circumference of a Circle = Area of the circle ... (i)
We know that, for a circle:
$$Area\ =\ \pi r^2$$
$$Circumference=2\pi r$$
Plugging in the formulas of area and circumference of the circle in eq(i),
$$\pi r^2=2\pi r$$
$$r^2=2r$$
$$\frac{r^2}{r}=2$$
$$r=2$$
Therefore, the radius of the circle is 2.
We know that diameter is 2 times the radius, hence,
$$Diameter=2r=2\left(2\right)=4$$
Therefore, Option
C is correct.
Hope it helps.
I am available if you'd like any follow up.
