Question

3
the area of the circle above is 1,384.74 units². what is the circumference of the circle? (use 3.14 for π.)
a. 461.58 units
b. 692.37 units
c. 65.94 units
d. 131.88 units

Explanation:

Step1: Recall the area formula of a circle

The area formula of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We know \( A = 1384.74 \) and \( \pi=3.14 \), so we can solve for \( r \).

$$ 3.14\times r^{2}=1384.74 $$

Step2: Solve for the radius \( r \)

First, divide both sides of the equation by \( 3.14 \):

$$ r^{2}=\frac{1384.74}{3.14}=441 $$

Then, take the square root of both sides. Since the radius is positive, we have \( r = \sqrt{441}=21 \).

Step3: Recall the circumference formula of a circle

The circumference formula of a circle is \( C = 2\pi r \), where \( C \) is the circumference. Now we know \( r = 21 \) and \( \pi = 3.14 \), substitute these values into the formula.

$$ C=2\times3.14\times21 $$

Step4: Calculate the circumference

First, calculate \( 2\times3.14 = 6.28 \), then calculate \( 6.28\times21=131.88 \).

Answer:

D. 131.88 units