Question

A circle has a circumference of 2 pi cm. Which statement about the circumference and area is true? A comparison of the area and circumference is not possible since the area cannot be determined. The numerical values of the circumference and area of the circle are equal. The numerical value of the circumference is greater than the numerical value of the area. The numerical value of the circumference is less than the numerical value of the area.

Answer 1

Answer:

Third option: The numerical value of the circumference is greater than the numerical value of the area.

Step-by-step explanation:

The  area of a circle can be calculated with this formula:

$A=\pi r^2$

Where "r" is the radius of the circle.

The  circumference of a circle can be calculated with this formula:

$C=2\pi r$

Where "r" is the radius of the circle.

 In this case you know that:

$C=2\pi \ cm$

Then, if you subsitute this value into the formula $C=2\pi r$  and you solve for "r", you get that the radius of the circle is:

$2\pi \ cm=2\pi r\\\\r=\frac{ 2\pi \ cm}{2\pi} \\\\r=1\ cm$

Then, substituting the radius into the formula for calculate the area of a circle adn evaluating, you get that its area is:

$A=\pi (1\ cm)^2\\\\A=\pi \ cm^2$

Based on the obtained, you can identify that:

$2\pi >\pi$

Therefore, the numerical value of the circumference is greater than the numerical value of the area.

Answer 2

Answer:

C: The numerical value of the circumference is greater than the numerical value of the area.

Step-by-step explanation: