Question

Can someone help me with this problem?
A carnival ride is in the shape of a wheel with a radius of 30 feet. The wheel has 30 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

@robtobey can you help?

Answer 2

Ok, there are 360 degrees in a circle (or 2pi radians). So since there are 30 cars, each angle is 360 degrees/30, or 2pi/30

Answer 3

so i would divide 360by30?

Answer 4

Yes.

Answer 5

12

Answer 6

Yes, I think that's what they're asking for when they say central angle.

Answer 7

And it's 12 degrees.

Answer 8

Do you know how to find arc length?

Answer 9

No.. sorry

Answer 10

@anthonyym how do i find the arc length

Answer 11

Do you know what radians are?

Answer 12

They sound familiar.

Answer 13

Have you been taught that yet?

Answer 14

Maybe i am not sure.

Answer 15

Well, arc length formula is
\[S = \theta r\]
S is arc length,
θ (theta) is angle,
r is radius.

And theta is in radians.

Answer 16

oh yes! i remember that.

Answer 17

So to convert the angle to radians (it's currently 12 degrees), you multiply by 2pi/360, or pi/180.

Answer 18

\[\frac{ 12° }{ 1 }*\frac{ \pi }{ 180° }\]

Answer 19

ok so i would do 12x3.14 and 1x180 right?

Answer 20

Yes, in other words (12pi)/180

Answer 21

Ok

Answer 22

Or, you could have found the angle in radians from the beginning. A circle is 360 degrees, or 2pi radians. So you could have found the angle between each car in radians by doing (2pi)/30

Answer 23

so is 12pi/180 the arc length?

Answer 24

No, that's the angle in radians

Answer 25

oh ok.

Answer 26

To find arc length, the formula is S=angle[in radians]*radius, where S is the arc length.

Answer 27

We converted the angle to radians because it was in degrees and the formula requires the angle to be in radians.

Answer 28

Oh ok that makes sense