Question

1. what is the circumference, in inches, of a circle with a radius of 8 inches?

a. 4π
b. 8π
c. 12π
d. 16π
e. 64π

1. the circle shown below has a diameter of 14 inches. what is the circumference of the circle, in inches?

f. 7π
g. 14π
h. 28π
j. 49π
k. 196π

1. the perimeter of a circular field is 500 feet. which of the following is closest to the radius of the field, in feet? (note: π≈3.14)

a. 10
b. 50
c. 80
d. 160
e. 250

Explanation:

Question 1

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C = 2\pi r\), where \(r\) is the radius.

Step2: Substitute the radius value

Given \(r = 8\) inches. Substitute into the formula: \(C=2\pi\times8 = 16\pi\) inches.

Question 2

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter.

Step2: Substitute the diameter value

Given \(d = 14\) inches. Substitute into the formula: \(C=\pi\times14=14\pi\) inches.

Question 3

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C = 2\pi r\). We know \(C = 500\) feet and \(\pi\approx3.14\).

Step2: Solve for \(r\)

From \(C = 2\pi r\), we can express \(r=\frac{C}{2\pi}\). Substitute \(C = 500\) and \(\pi = 3.14\): \(r=\frac{500}{2\times3.14}=\frac{500}{6.28}\approx79.62\approx80\) feet.

Answer:

1. D. \(16\pi\)
2. G. \(14\pi\)
3. C. \(80\)