A carnival ride is in the shape of a wheel with a radius of 15 feet. The wheel has 24 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

dontknowdontcare · Answer

@jabez177 do you know thus?

dontknowdontcare · Answer

@mrm @Mehek14

anthonyym · Answer

The central angle would be 360 degrees divided by how many cars.

dontknowdontcare · Answer

Okay, so 15 is the central angle

dontknowdontcare · Answer

how do I find the arc length?

anthonyym · Answer

Arc length is 
S = theta*r,
where the angle theta is in radians

dontknowdontcare · Answer

Could I find it with what information is given?

anthonyym · Answer

So the arc length using degrees would be
S = (pi/180)*theta*r

Because multiplying by pi/180 converts an angle in degrees to radians.

dontknowdontcare · Answer

And what is theta here?

anthonyym · Answer

theta is the central angle 15 degrees, and r is radius.

dontknowdontcare · Answer

Would it be 225?

dontknowdontcare · Answer

@anthonyym

anthonyym · Answer

No.
You have $$\frac{ \pi }{ 180 }*15*15$$.
And also the circumference is 94.25 feet, so an arc length of that can't be larger.

dontknowdontcare · Answer

I got 3.925?

dontknowdontcare · Answer

@anthonyym

anthonyym · Answer

Yes good.
Now for the area between the two cars, it would be 
theta/360 * pi*r^2

anthonyym · Answer

theta is still the central angle