Problem Solving

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?

ardz24 wrote: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

C = 2Ï€r.
A = πr².

Since C=A, we get:
2πr = π r²
2r = r²
2 = r.
Thus, d = 2r = 2*2 = 4.

The correct answer is C.

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.