Question

a circle has a diameter of 4 inches. which statement about the area and circumference of the circle is true?

a comparison of the area and circumference of the circle is not possible because there is not enough information to find both.
the numerical values of the circumference and area 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.

Explanation:

Calculate the radius from the diameter

$$ r = \frac{d}{2} = \frac{4}{2} = 2\text{ inches} $$

Calculate the circumference of the circle

$$ C = 2\pi r = 2\pi(2) = 4\pi\text{ inches} $$

Calculate the area of the circle

$$ A = \pi r^2 = \pi(2)^2 = 4\pi\text{ square inches} $$

Answer:

• A comparison of the area and circumference of the circle is not possible because there is not enough information to find both.
• The numerical values of the circumference and area are equal. (Correct answer)
• 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.