A carnival ride is in the shape of a wheel. 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?

Question

damien_gannon123 · Answer

I looked around and the only answers I found were questions that contained the radius... Is that the only way to find the arc length?

lord_box · Answer

Yes, you need the radius. theta = arc length/radius, so arc length = theta * radius, which means the arc length depends on the radius.

damien_gannon123 · Answer

But they don't give me the radius >.>

lord_box · Answer

You could put your answer in terms of the radius.

damien_gannon123 · Answer

how would I do that?

lord_box · Answer

You've probably seen something like this before. It's the same concept, except with r instead of pi.$$36\pi$$

damien_gannon123 · Answer

ok so to find the arc length i do center angle * radius?

damien_gannon123 · Answer

so it would be 22.5(radius)

lord_box · Answer

Careful, theta needs to be the radian measure of the angle.

damien_gannon123 · Answer

I'm confused

lord_box · Answer

You've solved the first part already, 22.5 which is great. But this value is in degrees. the equation: $$s = r * \theta$$ requires the angle to be in radians.

damien_gannon123 · Answer

0.3926991?

lord_box · Answer

That's right.

damien_gannon123 · Answer

so 0.3926991(radius) would be center angle?

damien_gannon123 · Answer

i mean arc length oops

lord_box · Answer

Yep, arc length.

damien_gannon123 · Answer

so how would I find the area between two cars from that?

lord_box · Answer

Well first off, what's the area formula for a circle?

damien_gannon123 · Answer

A=$$\pi$$*r^2 right

damien_gannon123 · Answer

why it go sepearte lines >.>

lord_box · Answer

Right. Now, the space between cars isn't the whole circle, but a fraction of it. What fraction would that be?

damien_gannon123 · Answer

idk im confused

lord_box · Answer

Well there are 16 spaces total. It wants you to find the area of only one of them, so what fraction of the circle's area would you need?

damien_gannon123 · Answer

oh I'm stupid i see now so we're finding 1/16th of the area?

damien_gannon123 · Answer

so A = (pi*r^2)/16?

lord_box · Answer

That's right.

damien_gannon123 · Answer

how would I simplify that if I don't have the radius?

lord_box · Answer

You can't, unfortunately.

damien_gannon123 · Answer

ok I think I have what I need thank you for the help