Question

3.(09.04 MC)A camival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. What is the central angle,arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work

Answer 1

We are given that a wheel ride has 20 cars attached to it. To determine the arclength we need to determine the angle that there is between each of the cars. To do that we use the fact that the entire wheel has an angle of:

`\theta_(Total)=2\pi`

Since there are 20 cars we need to divide the total angle by 20 to determine the angle between each car:

`\theta=(\theta_(total))/(20)=(2\pi)/(20)=(\pi)/(10)`

Now, the arc length can be determined using the following formula:

`S=r\theta`

Where:

`\begin{gathered} S=\text{ arc length} \\ r=\text{ radius} \\ \theta=\text{ angle} \end{gathered}`

Substituting the values we get:

`S=(25ft)((\pi)/(10))`

Solving the operations we get:

`S=7.85ft`

Therefore, the arclength is 7.85 ft.

Now, to determine the area of the sector we use the following formula:

`A=(1)/(2)r^2\theta`

Substituting we get: