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:
[tex]C=2\pi r[/tex]
Where:
C is the circumference.
r is the radius = 4 inches.
Plug in 4 for r and solve for r:
[tex]\begin{gathered} C=2\pi *4 \\ \\ C=25.1\text{ inches} \end{gathered}[/tex]
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:
[tex]\begin{gathered} L=2\pi r*\frac{\theta}{360} \\ \\ L=C*\frac{\theta}{360} \end{gathered}[/tex]
Where:
θ is the central angle = 60 degrees.
C is the circumference.
Thus, we have:
[tex]\begin{gathered} L=25.1*\frac{60}{360} \\ \\ L=25.1*\frac{1}{6} \\ \\ L=4.18\approx4.2\text{ inches} \end{gathered}[/tex]
Therefore, the length of the arc is 4.2 inches.
ANSWER:
• (A). 25.1 inches
• (B). 4.2 inches
