A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground?

= ? PI inches

Question

A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground?

= ? PI inches

radar · Answer

If the wheel rotated 360 degrees the distance would be the circumference or$$2\pi26 $$inches.  However it did not rotate 360 but only 80 degrees.  We can now set up a proportion:

80:360::x:52pi   solving by the product of the means = product of the extremes we have:
360x=80(52)(pi)
360x=4160 pi
x=11.555 pi

radar · Answer

Rounding off it is about 36.3 inches

radar · Answer

Is that one of your options?  what is the 7 Pi inches, is that one of the choices?

poppylizzie · Answer

It says that It is incorrect...I have tried to complete this problem multiple times and keep getting it wrong. It's just frustrating not being able to get it right. And It doesn't have any choices...it's just a blank.

radar · Answer

Well I have double checked and I am satisfied with that answer.  Be sure to include the unit inches in your answer     11.555 Pi In.

radar · Answer

Something to note.  Bicycle wheels would normally have 26 in. diameter (not radius)  Read the problem again and see if the 26" is the diameter.

poppylizzie · Answer

It says "radius 26" I sent my teacher a note...it could just be the system... Thank you so much for taking time to explain this to me. :)

radar · Answer

You're welcome, I feel your pain, but don't know how to fix it.