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

Step-by-step 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=(10)/(15)=(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

Step-by-step explanation

Here, central angle =
`(\pi)/(2)` radians and radius = 8

So, plugging
`\theta=(\pi)/(2)` and
`r=8` into the formula....

`S= 8*(\pi)/(2)\\ \\ S=4\pi=4(3.14)=12.56`

Thus, the length of the arc will be 12.56