The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians?

A. 3/11
B. 6/11
C. 11/6
D. 11/3

Question

The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians?

A. 3/11
B. 6/11
C. 11/6
D. 11/3

Dylan Arnold · Accepted Answer

D #11/3# Circumference=#piD# Arc length=#theta/(2pi)xxpiD# #33=theta/(2pi)xx18pi# #33=9theta# #theta=33/9=11/3#

Charles Autterson · Answer

undefined To find the measure of angle $ \theta $ in radians, we can use the formula for arc length in radians.

Given that the diameter of the circle is 18 centimeters, the radius (denoted as $ r $) is half of the diameter, which is $ \frac{18}{2} = 9 $ centimeters.

The formula for arc length ($ s $) in radians is:

$$ s = r \cdot \theta $$

where:
- $ s $ is the arc length,
- $ r $ is the radius of the circle,
- $ \theta $ is the angle in radians.

We're given that the arc length is 33 centimeters. Substituting the given values into the formula, we can solve for $ \theta $:

$$ 33 = 9 \cdot \theta $$

$$ \theta = \frac{33}{9} $$

$$ \theta \approx 3.67 $$

So, the measure of angle $ \theta $ in radians is approximately $ 3.67 $ radians.

The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians?

The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians? A. 3/11 B. 6/11 C. 11/6 D. 11/3

The circle shown below has a diameter of 18 centimeters (cm). If the dotted arc is 33 cm long, what is the measure of angle θ in radians?

A. 3/11
B. 6/11
C. 11/6
D. 11/3