Answer:
We will find the arc length of the given circles.
By using[tex]\theta=\frac{s}{r}[/tex]
And also [tex]degree=\frac{\pi}{180}radian[/tex]
Where, s is the arc length and r is the radius.
In figure 3 : radius is 9 yd and [tex]\theta=45^{\circ}[/tex]
On substituting the values in the formula we get:
[tex]45^{\circ}=\frac{s}{9}[/tex]
[tex]s=\frac{9\pi}{4}[/tex]
In figure 4:radius is 11 km and [tex]\theta=150^{\circ}[/tex]
On substituting the values in the formula we get:
[tex]150^{\circ}=\frac{s}{11}[/tex]
[tex]150\cdot \frac{\pi}{180}=\frac{s}{11}[/tex]
[tex]\Rightarrow \frac{5\pi}{6}=\frac{s}{11}[/tex]
[tex]\Rightarrow \frac{55\pi}{6}=s[/tex]
In figure 5:radius is 11 in and [tex]\theta=270^{\circ}[/tex]
On substituting the values in the formula we get:
[tex]270^{\circ}=\frac{s}{11}[/tex]
[tex]270\cdot \frac{\pi}{180}=\frac{s}{11}[/tex]
[tex]\Rightarrow \frac{3\pi}{2}=\frac{s}{11}[/tex]
[tex]\Rightarrow \frac{33\pi}{2}=s[/tex]
In figure 5:radius is 11 in and [tex]\theta=270^{\circ}[/tex]
On substituting the values in the formula we get:
[tex]270^{\circ}=\frac{s}{11}[/tex]
[tex]270\cdot \frac{\pi}{180}=\frac{s}{11}[/tex]
[tex]\Rightarrow \frac{3\pi}{2}=\frac{s}{11}[/tex]
[tex]\Rightarrow \frac{33\pi}{2}=s[/tex]
In figure 6:radius is 7 in and [tex]\theta=150^{\circ}[/tex]
On substituting the values in the formula we get:
[tex]150^{\circ}=\frac{s}{7}[/tex]
[tex]150\cdot \frac{\pi}{180}=\frac{s}{7}[/tex]
[tex]\Rightarrow \frac{5\pi}{6}=\frac{s}{7}[/tex]
[tex]\Rightarrow \frac{35\pi}{6}=s[/tex]
