It takes ten identical pices to form a circular track for a pair of toy racing cars. If the inside arc of each pair is 3.4 inches shorter than the outside arc, what is the width of the track?
any help would be greatly appreciated.
If you know that the circumference is C=2pi*r where r is the radius, then the total difference between the inside and outside radii is 10*3.4=34in. This means 2pi*r+34=2pi*R where r and R are the inner and outer radii respectively. Note that R-r is the track width.
Thus 34=2pi*R-2pi*r= 2pi(R-r) so
34/(2*pi) = R-r = track width
To solve this problem, we need to use the formula for the circumference of a circle, which is C = 2πr, where C represents the circumference and r represents the radius.
Let's assume that the inside radius of the track is r. Since the inside arc is 3.4 inches shorter than the outside arc, the outside radius would be r + 3.4.
Now, we need to calculate the total difference between the inside and outside radii. Since there are ten identical pieces, the total difference would be 10 * 3.4 = 34 inches.
Using the circumference formula, we can set up the equation:
2πr + 34 = 2π(r + 3.4)
By simplifying the equation, we get:
2πr + 34 = 2πr + 2π(3.4)
34 = 2π(3.4)
To find the track width (R - r), we can calculate R - r using the equation:
R - r = 34 / (2π)
Simplifying this equation, we get:
R - r = 17 / π
Therefore, the width of the track is 17 / π inches.