Question

It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track?

Answer 1

let r_i be the inner track and r_o be the outer track
each piece has one-tenth of a circle so\[\theta=\frac{2\pi}{10}=\frac{\pi}{5}\]and for the track we have\[r_0\theta=r
_i\theta+3.4\to (r_o-r_i)\theta=3.4\to r_o-r_i=\frac{3.4}{\theta}\]where r_o-r_i is the width of the track

Answer 2

thank you so much!! can you just tell me how you got 2pi over 10?

Answer 3

that is the angle subtended by each piece of track
the whole circle is 2pi radians
a tenth of it is 2pi/10 radians
(because there are ten pieces of track)

Answer 4

ohhh ok thanks

Answer 5

you're welcome :)