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.

Question

imstuck · Answer

This will be fun!  Let's draw a pic!

anonymous · Answer

Okay! haha :)

imstuck · Answer

|dw:1403661822263:dw|

imstuck · Answer

That is such a lovely piece of artwork is it not?

anonymous · Answer

I love it!

imstuck · Answer

This is a shabby-looking example of our carnival ride.  Each length from the center to the outside is 25 ft.  That's what you're given.

imstuck · Answer

I think I'll patent it and sell it.

anonymous · Answer

Lol! And alright, I'm following along.

imstuck · Answer

The want to know the central angle, right?  Do you know how a central angle is found?  A circle has a measure of 360 degrees.  We have 20 angles in that circle.  What does one angle measure, then?

anonymous · Answer

360/20?

imstuck · Answer

Yep!  What does that come out to?

anonymous · Answer

18

imstuck · Answer

Very good!  Now do you know how central angles relate to their arcs?

anonymous · Answer

Nope!

imstuck · Answer

Ok, well I am going to tell you and don't forget ok, cuz this is important and you will continue to use this fact throughout your years of math.  The formula to find the arc length (which is not the same as the arc measure) is |dw:1403662509727:dw|

anonymous · Answer

Oh, I see! gotchu!!

imstuck · Answer

Here we don't know the arc length so we fill in everything we do know and solve for the length.|dw:1403662608805:dw|

anonymous · Answer

Mmhm..I am following you

imstuck · Answer

18 is the MEASURE of the arc which is equivalent to the central angle's measure.  Now we are finding arc LENGTH.  Two different thing, totally!  What do you get for the arc length, then?

anonymous · Answer

7.85!

imstuck · Answer

That is correct unless you have to leave your answer in terms of pi, which is 2.5pi, then.  Either way, yes, you are correct!  Good!

imstuck · Answer

Now for the area of the sector.....

anonymous · Answer

Oh ok, yay!! :)) thanks!

anonymous · Answer

yup

imstuck · Answer

That also has a formula, of course.  Cuz this is math and what fun would it be if there wasn't yet another formula?!

anonymous · Answer

haha -_- lol
its's 
x/360 = pi r^2

anonymous · Answer

oops I meant multiply8

anonymous · Answer

multiply* LOl

imstuck · Answer

The area formula for a sector of our circle is as follows:
18/360 * pi* r^2.  You're right.  So what would that be?

anonymous · Answer

98.17

imstuck · Answer

Perfect!  See!?  It must have been my awesome drawing...

imstuck · Answer

Good job!

anonymous · Answer

of course oh yeah!! totally was :) thank you! :)))))))))