Question

Find the length of CD.express the awnser as a fraction times pie.

Answer 1

Given the figure of the circle B

the radius of the circle = r = BC = 9

the measure of the angle CBD = 40°

We will find the length of the arc CD

The length of the arc is given by the formula:

`l=\theta\cdot r`

where: θ is the central angle opposite to the arc measured in radians

so, we will convert the given angle from degree to radian

`\theta=40\cdot(\pi)/(180)=(2)/(9)\pi`

Substitute with the given values

so, the length of the arc =

`l=(2)/(9)\pi\cdot9=2\pi`

So, the answer will be:

The length of the arc CD = 2π