Question

a circle has a radius of 18 cm. what is the length of an arc that has a measure of 90°?
a 9π cm
b 10π cm
c 28π cm
d 14π cm

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360^{\circ}}\times2\pi r\), where \(\theta\) is the central angle of the arc and \(r\) is the radius of the circle.

Step2: Substitute the given values

Given \(r = 18\mathrm{cm}\) and \(\theta=90^{\circ}\).
Substitute into the formula: \(s=\frac{90^{\circ}}{360^{\circ}}\times2\pi\times18\).
Simplify \(\frac{90^{\circ}}{360^{\circ}}=\frac{1}{4}\).
Then \(s=\frac{1}{4}\times2\pi\times18\).
First, calculate \(\frac{1}{4}\times2=\frac{1}{2}\).
Then \(s=\frac{1}{2}\times18\pi\).
Since \(\frac{1}{2}\times18 = 9\), so \(s = 9\pi\mathrm{cm}\).

Answer:

A. \(9\pi\mathrm{cm}\)