Question

A carnival 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. Use 3.14 for pi and round answers to the nearest hundredth, if applicable.a.) What is the measure of each central angle between any two cars? (4 points)b.) What is the arc length of each sector between any two cars? (4 points)c.) What is the area of each sector between any two cars?

Answer 1

The carnival ride is in shape of wheel with 25ft radius.

The wheel has 20 cars attached to the center of the wheel. Since the cars are evenly distributed, we can thus find the

the measure of the angle between each car by dividing 360 degrees by 20.

#A:

The measure of each central angle between any two cars is:

`(360)/(20)=18^0`

#B:

Hence, we can find the length of the arch between any two cars is given by the length of arc formula given below:

`\begin{gathered} (\theta)/(360)*2\pi r \\ \text{where,} \\ r=\text{radius} \\ \theta=\text{measure of each central angle betw}een\text{ two cars} \end{gathered}`

Let us calculate this length below:

`\begin{gathered} \theta=18^0 \\ (18)/(360)*2\pi*25 \\ =2.5\pi=7.85\text{ (to the nearest hundredth)} \end{gathered}`

#C:

We are asked to find the area of each sector between two cars.

The area of a sector of a circle is:

`(\theta)/(360)*\pi* r^2`

Since we have all the parameters, let us calculate this area:

`\begin{gathered} Area=(18)/(360)*\pi*25^2 \\ \\ Area=98.13\text{ (to nearest hundredth)} \end{gathered}`

Therefore, the final answers are:

#A: angle = 18 degrees

#B length = 7.85 feet

#C Area = 98.13 squared feet