Question

A) Find the circumference of a circle whose radius is 4 inches.Round to the nearest tenth.B) Find the length of AB, if m

Answer 1

Given:

• Radius of the circle, r = 4 inches

,

• Central angle, m∠ACB = 60 degrees

Let's solve for the following:

• (A). Find the circumference of a circle whose radius is 4 inches.

To find the circumference, apply the formula:

`C=2\pi r`

Where:

C is the circumference.

r is the radius = 4 inches.

Plug in 4 for r and solve for r:

`\begin{gathered} C=2\pi *4 \\ \\ C=25.1\text{ inches} \end{gathered}`

Therefore, the circumference of the circle is 25.1 inches.

• (B). Let's find the length of the arc AB.

To find the length of the arc AB, apply the formula:

`\begin{gathered} L=2\pi r*(\theta)/(360) \\ \\ L=C*(\theta)/(360) \end{gathered}`

Where:

θ is the central angle = 60 degrees.

C is the circumference.

Thus, we have:

`\begin{gathered} L=25.1*(60)/(360) \\ \\ L=25.1*(1)/(6) \\ \\ L=4.18\approx4.2\text{ inches} \end{gathered}`

Therefore, the length of the arc is 4.2 inches.

ANSWER:

• (A). 25.1 inches

• (B). 4.2 inches