Question

3 multiple choice 1 point a circle has a circumference of 16 cm. the measure of a central angle of the circle is 90 degrees. what is the length of the arc associated with this angle? 2 cm 4 cm 12 cm 8 cm 4 multiple choice 1 point the radius of a circular table is 13 inches. what is the diameter of the table? 13 inches 15 inches 26 inches 6.5 inches 5 multiple choice 1 point

Explanation:

Step1: Calculate the arc length proportion

The total degrees in a circle is \(360^{\circ}\). The central angle is \(90^{\circ}\), so the proportion of the arc is \(\frac{90}{360}=\frac{1}{4}\).

Step2: Find the arc length

The circumference of the circle is \(C = 16\mathrm{cm}\). The arc length \(l\) is the proportion of the circumference, so \(l=\frac{1}{4}\times16\).

Step1: Use the radius - diameter relationship

The formula for the diameter \(d\) of a circle in terms of the radius \(r\) is \(d = 2r\).

Step2: Substitute the given radius

Given \(r=13\mathrm{inches}\), then \(d=2\times13\).

Answer:

\(4\mathrm{cm}\)