Question

Fan and medal!!! helpppp :)
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

@TheSmartOne

Answer 2

@AaronAndyson

Answer 3

@mathstudent55

Answer 4

First,draw diagram.

Answer 5

A circle has 360 angles and we have 20 angles in that circle.

Answer 6

18?

Answer 7

Yes!

Answer 8

Do you know how central angle relates to the arc length?

Answer 9

no not really

Answer 10

arch length = radius*central angle

Answer 11

\[S = r \theta \]

Answer 12

r is given as 25.
Central we just calculated.

Answer 13

ok so now what do we do?

Answer 14

Wait.

Answer 15

Calculate the circumference of the circle.

Answer 16

\[C = 2 \pi r\]
r = 25

Substitute the values in:
\[C = 2 \pi \times 25\]
\[C = 50 \pi\]

Answer 17

that would be the answer? or is there more to it?

Answer 18

There is more to it.

Answer 19

Now,use this formula:
arch length = \[2 \pi r \times \frac{ A }{ 360 }\]
A = central angle.

Answer 20

Put in the values of and solve.

Answer 21

so a = 18?

Answer 22

what does x=?

Answer 23

Yes we calculated the value of A in a few steps above.

Answer 24

what does x and r = ??

Answer 25

im blind lol what does r = ?

Answer 26

i multiplied them all and got 3140 @AaronAndyson

Answer 27

arch length = \[\frac{ \theta }{ 360 } \times C\]
C = \[50 \pi\]

Answer 28

\[\theta = 18\]

Answer 29

i got to put this all into a response could you help me do that?

Answer 30

Its substitution man!
arch length =
\[\frac{ \theta }{ 360 } \times C\]
\[\frac{ 18 }{ 360 } \times 50 \pi\]
\[\frac{ 50 \pi }{ 20 }\]

So thats,
\[2.5 \pi\]

Answer 31

Now,area of sector is :
\[\frac{ \theta }{ 360 } \times \pi r^2\]

Answer 32

im terrible at man and never liked doing it but i have to and it dont make sense

Answer 33

so what would i put in the box as a response big part of my grades

Answer 34

\[\frac{ \theta }{ 360 } \times \pi r^2\]
\[\frac{ 18 }{ 360 } \times \pi (25)^2\]
\[\frac{ 625 \pi }{ 20 }\]
\[31.25 \pi\]

pi = 3.14

31.25*pi
= 31.25*3.14
= 98.125 sq feet

Answer 35

and arch length = 2.5*pi feet.