Question

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

Answer 1

We will find the arc length of the given circles.

By using
`\theta=(s)/(r)`

And also
`degree=(\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)=(s)/(9)`

`s=(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)=(s)/(11)`

`150\cdot (\pi)/(180)=(s)/(11)`

`\Rightarrow (5\pi)/(6)=(s)/(11)`

`\Rightarrow (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)=(s)/(11)`

`270\cdot (\pi)/(180)=(s)/(11)`

`\Rightarrow (3\pi)/(2)=(s)/(11)`

`\Rightarrow (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)=(s)/(11)`

`270\cdot (\pi)/(180)=(s)/(11)`

`\Rightarrow (3\pi)/(2)=(s)/(11)`

`\Rightarrow (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)=(s)/(7)`

`150\cdot (\pi)/(180)=(s)/(7)`

`\Rightarrow (5\pi)/(6)=(s)/(7)`

`\Rightarrow (35\pi)/(6)=s`