Question

I need help please! All answers must have pi in it.

Answer 1

Answer:

We will find the arc length of the given circles.

By using$\theta=\frac{s}{r}$

And also $degree=\frac{\pi}{180}radian$

Where, s is the arc length and r is the radius.

In  figure 3 : radius is 9 yd and $\theta=45^{\circ}$

On substituting the values in the formula we get:

$45^{\circ}=\frac{s}{9}$

$s=\frac{9\pi}{4}$

In figure 4:radius is 11 km and $\theta=150^{\circ}$

On substituting the values in the formula we get:

$150^{\circ}=\frac{s}{11}$

$150\cdot \frac{\pi}{180}=\frac{s}{11}$

$\Rightarrow \frac{5\pi}{6}=\frac{s}{11}$

$\Rightarrow \frac{55\pi}{6}=s$

In figure 5:radius is 11 in and $\theta=270^{\circ}$

On substituting the values in the formula we get:

$270^{\circ}=\frac{s}{11}$

$270\cdot \frac{\pi}{180}=\frac{s}{11}$

$\Rightarrow \frac{3\pi}{2}=\frac{s}{11}$

$\Rightarrow \frac{33\pi}{2}=s$

In figure 5:radius is 11 in and $\theta=270^{\circ}$

On substituting the values in the formula we get:

$270^{\circ}=\frac{s}{11}$

$270\cdot \frac{\pi}{180}=\frac{s}{11}$

$\Rightarrow \frac{3\pi}{2}=\frac{s}{11}$

$\Rightarrow \frac{33\pi}{2}=s$

In figure 6:radius is 7 in and $\theta=150^{\circ}$

On substituting the values in the formula we get:

$150^{\circ}=\frac{s}{7}$

$150\cdot \frac{\pi}{180}=\frac{s}{7}$

$\Rightarrow \frac{5\pi}{6}=\frac{s}{7}$

$\Rightarrow \frac{35\pi}{6}=s$