A carnival ride is in the shape of a wheel with a radius of 20 feet. The wheel has 16 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

anonymous · Answer

@ganeshie8

anonymous · Answer

@Preetha

anonymous · Answer

@campbell_st  please help! its my last question

campbell_st · Answer

ok... to find the sector angle... there are 20 cars... 

and 360 degrees in a circle

so the sector angle is 

sector angle = 360/20

the fraction of a circle created by each sector is 

sector angle/360... you need this for the next 2 parts

arc length = fraction x circumference

area of sector = fraction x area of the circle. 

hope it helps

anonymous · Answer

Thank you!

anonymous · Answer

I got 22.5 for the first part

anonymous · Answer

So I have to divide that again by 360?

campbell_st · Answer

hold on I just re-read the question... the sector angle is 

360/16

yep thats the sector angle... 

so the fraction of the circle is 

22.5/360

which you need for area and arc length

anonymous · Answer

Okay!

anonymous · Answer

I got 0.0625, so now what do I do?

campbell_st · Answer

so I'd leave it as a fraction 

arc length.... 

$$l = \frac{22.5}{360} \times 2 \times \pi \times r$$

substitute the radius of 20... and then calculate

area of the sector

$$A = \frac{22.5}{360} \times \pi \times r^2$$

again substitute r = 20 and calculate

anonymous · Answer

Okay I think i got it so far! Ill msg you my final result and you see how it looks like?

campbell_st · Answer

so when you get the answers, round them to 2 decimal places... and include the units... arc length ft

area ft^2

anonymous · Answer

I got 7.85 as the arc length

anonymous · Answer

And the area sector as 78.5

anonymous · Answer

How do I find the central angle?

anonymous · Answer

nvm i got it