Question

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.

Answer 1

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?

Answer 2

18

Answer 3

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

\(\bf \textit{arc's length}=\cfrac{r\theta\pi }{180}\qquad
\begin{cases}
r=25\\
\theta=18
\end{cases}\implies \cfrac{25\cdot 18\cdot \pi }{180}\)

Answer 4

to get the sector of that radius, with that angle

\(\bf \textit{sector of a circle}=\cfrac{r^2\theta\pi }{360}\qquad
\begin{cases}
r=25\\
\theta=18
\end{cases}\implies \cfrac{25^2\cdot 18\cdot \pi }{360}\)

Answer 5

okay so would the answer for arc length be 0.43?

Answer 6

and the sector would it be 98.17?

Answer 7

hmmm ahemm nope

https://www.google.com/search?client=opera&q=25*18*pi/180&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest&gws_rd=ssl

Answer 8

98.17 for the sector is correct

Answer 9

thank you so much thats it right?

Answer 10

yeap

Answer 11

okay can you help me with another problem please

Answer 12

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

Answer 13

okay i will