Question

REALLY REALLY NEED HELP WITH THIS
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

PLEASE HELP

Answer 2

let's say there are 2 cars equally spaced apart (and only two cars)

what's the central angle?

Answer 3

180? @jim_thompson5910

Answer 4

how did you calculate that

Answer 5

because there are 2 cars and the degrees of circle is 360 so 360/2 is 180

Answer 6

good, so with 20 cars, you'd have 360/20 = 18 degrees as the central angle (between two adjacent cars)

Answer 7

what's the circumference of this whole circle?

Answer 8

okay I got that part

Answer 9

idk the circumference idk how to get that :(

Answer 10

use the formula

C = 2*pi*r

Answer 11

okay so 157

Answer 12

I'd leave it in terms of pi

Answer 13

actually they want you to "Round answers to the nearest hundredth if applicable"

Answer 14

but that's not the answer, so leave it in terms of pi for now

C = 2*pi*r

C = 2*pi*25

C = 50pi

That's the exact circumference

Answer 15

whats terms of pi? I thought the answer was 157

Answer 16

the arc length between two adjacent cars is going to be 18/360 = 1/20 of the whole circumference (ie we're cutting up the perimeter of the circle into twenty equal pieces)

Answer 17

so

(1/20)*50pi = (50/20)*pi = (5/2)*pi

is the exact arc length between two adjacent cars

Answer 18

but why don't we just use 3.14 for pi since it says round? its not asking for an exact answer

Answer 19

alright, go ahead and use the approximation pi = 3.14

Answer 20

so would the arc length be 7.85

Answer 21

157/20 ?

Answer 22

157 is close, but not quite the circumference

Answer 23

so I wouldn't use 157

Answer 24

7.85 is what I'm getting for the arc length

Answer 25

What is the area of the circle?

Answer 26

idk the area I have no clue how to get it

Answer 27

use

A = pi*r^2

Answer 28

1962.5?

Answer 29

roughly, yes

Answer 30

now divide that by 20 to split the whole circle into 20 equal pieces (or slices)

Answer 31

this will give you the rough area of the sector

Answer 32

so again,

the arc length is found by dividing the circumference by 20
the area of the sector is found by dividing the area by 20

Answer 33

okay cool thanks

Answer 34

and whats the central angle?

Answer 35

it's shown above when we divided the 360 degrees into 20 equal pieces

Answer 36

oh okay thank you

Answer 37

np

Answer 38

i have a few more questions, can i tag you in them for help?