anonymous one year ago will give medal and fan please help 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. 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 and calculations to receive credit.

1. jdoe0001

so the wheel with 20 cars looks like http://www.uer.ca/forumpic/perspic/c2e2e83f7e21539f891d1e5e0723156f.jpg each car in each vertex, or corner keeping in mind that a circle has 360 degrees, how many degrees would there be between each vertex or corner, or in this case, each car?

2. anonymous

18

3. jdoe0001

yeap 360/20 is 18 so there's your central angle, 18 degrees :) now, we know the radius is 25 the central angle is 18 so, what's the arc's length? well $$\bf \textit{arc's length}=\cfrac{r\theta\pi }{180}\qquad \begin{cases} r=25\\ \theta=18 \end{cases}\implies \cfrac{25\cdot 18\cdot \pi }{180}$$

4. jdoe0001

to get the sector of that radius, with that angle $$\bf \textit{sector of a circle}=\cfrac{r^2\theta\pi }{360}\qquad \begin{cases} r=25\\ \theta=18 \end{cases}\implies \cfrac{25^2\cdot 18\cdot \pi }{360}$$

5. anonymous

okay so would the answer for arc length be 0.43?

6. anonymous

and the sector would it be 98.17?

7. jdoe0001
8. jdoe0001

98.17 for the sector is correct

9. anonymous

thank you so much thats it right?

10. jdoe0001

yeap

11. anonymous

okay can you help me with another problem please

12. jdoe0001

sure, just post a new, more eyes, thus if I dunno, someone else may know

13. anonymous

okay i will