Question

let s denote the length of the arc of a circle of radius r subtended by the central angle θ. find the missing quantityθ = 1/3 radian, s = 6 foot, r =?the radius r of the circle is foot (simplify your answer.)

Explanation:

Step1: Recall the arc - length formula

The formula for the arc length \(s\) of a circle is \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians.

Step2: Solve the formula for \(r\)

From \(s = r\theta\), we can isolate \(r\) by dividing both sides of the equation by \(\theta\). So \(r=\frac{s}{\theta}\).

Step3: Substitute the given values

We are given that \(s = 6\) feet and \(\theta=\frac{1}{3}\) radian. Substituting these values into the formula \(r=\frac{s}{\theta}\), we get \(r=\frac{6}{\frac{1}{3}}\).

Step4: Simplify the expression

Using the rule for dividing by a fraction (\(a\div\frac{b}{c}=a\times\frac{c}{b}\)), then \(r = 6\times3\).

Answer:

\(18\)