Question

In the circle to the left, segment ABABA, B is a diameter. If the length of arc \stackrel\frown{ADB} ADB ⌢ is 8 \pi8π8, pi, what is the length of the radius of the circle?

Answer 1

The length of the radius of the circle is 8 units

How to determine the length of the radius of the circle?

From the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

ADB = 8π

The length of an arc is calculated using

`\text{Arc Length} = (\theta)/(360) * 2\pi r`

In this case, we have

θ = 180 --- angle in a semicircle

So, we have

`(180)/(360) * 2\pi r = 8\pi`

This gives

`\pi r = 8\pi`

Divide

r = 8

Hence, the length of the radius of the circle is 8 units

Question

In the circle to the left, segment AB is a diameter. If the length of arc ADB is 8π, what is the length of the radius of the circle?

Answer 2

Answer: 4 units

Explanation:

Given : AB is the diameter of a circle.

Then, the central angle for arcADB must be
`2\pi` because the central angle subtended by diameter is
`2\pi` .

The length of arc is given by :-

`L=r*\theta\\\\\Rightarrow\  8\pi=r*2\pi\\\\\Rightarrow\ r=(8\pi)/(2\pi)=4`

Hence, the length of the radius of the circle = 4 units