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4 votes
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

User Ilanman
by
7.0k points

1 Answer

4 votes

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

User Bstakes
by
8.0k points
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