Question

What is the approximate measure, in radians, of the central angle of the circle whose radius is 15 m and arc length is 10 m?

0.67


1.5


2.6


0.37

Question 2 Unsaved
What is the length of the arc intercepted by a central angle of π/2 radians on a circle with radius 8? Use 3.14 for π and round your answer to the nearest hundredth, if necessary.

25.12


2.55


12.56


1.57

Answer 1

Formula for arc length is:   $S= r*\theta$ , where $S=$ Arc length, $r=$ radius of the circle and $\theta =$ central angle in radians.

Question 1

The correct option is:  0.67

Explanation

Here given that, radius is 15 meter and arc length is 10 meter.

So, plugging $r=15$ and $S=10$ into the above formula......

$10=15*\theta\\ \\ \theta=\frac{10}{15}=\frac{2}{3}=0.666... \approx 0.67$

Thus, the central angle of the circle is  0.67 radians.

Question 2

The correct option is:  12.56

Explanation

Here, central angle = $\frac{\pi}{2}$ radians and radius = 8

So, plugging $\theta=\frac{\pi}{2}$ and $r=8$ into the formula....

$S= 8*\frac{\pi}{2}\\ \\ S=4\pi=4(3.14)=12.56$

Thus, the length of the arc will be 12.56