Question

A circle has a radius of 8 and a central angle of 33 degrees. What is the arc length?

a) 22pi/15 radians
b) 9 pi radians
c) 6pi/9 radians
d) 15pi/22 radians

Answer 1

Given:-

• Arc of angle = 33°
• Radius = 8 cm

Find:-

• Length of arc??

Solution:-

Use Arc Length Formula,

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \therefore \text \: S = r \theta`

Now, we have to convert θ into radian, So we will multiply by (π/180).

`\: \: \: \: \: \rightarrow \text \: S = r \theta( ( \pi)/(180) ) \\ \\ \: \: \: \: \: \rightarrow S =8 * 33 * ( \pi)/(180) \\ \\ \: \: \: \: \: \rightarrow S = (22 \pi)/(15) radian`

So your First option is correct ✓✓

Answer 2

The arc length of the circle with a radius of 8 and a central angle of 33 degrees is approximately 22π/15 radians.

Step-by-step explanation:

The arc length of a circle can be calculated using the formula:

arc length = radius x central angle

In this case, the radius of the circle is 8 and the central angle is 33 degrees. We can plug these values into the formula to find the arc length:

arc length = 8 x 33 degrees

To convert from degrees to radians, we can use the formula:

radians = degrees x (π/180)

Plugging in the value of the central angle, we get:

radians = 33 x (π/180)

Simplifying, we find that the arc length is approximately 22π/15 radians.