REFLECTION

10. If a smaller replica of the Ferris wheel was constructed, what conclusions could you draw about the central angle of the original wheel and replica? What conclusions could you draw about the arc length of the original Ferris wheel and replica?

　

I believe that the radius and diameter would change because the wheel has been reduced. Since the radius has changed the arc length would also change. The central angle would probably stay the same because angle measurements stay the same in a dilation. The midpoint would also stay the same.

　

　

11. Imagine the center of the Ferris wheel is located at (0, 0) on a coordinate grid and the radius lies on the x-axis. Write an equation of a circle for your Ferris wheel and sketch an image of what your Ferris wheel would look like on the grid.

(x-0)^2 + (y - 0)^2 = 60^2

CALCULATIONS

1. Name of the Ferris wheel : The London Eye

2. Diameter of the wheel : 120m

3. # Carts: 32

4. Circumference of the wheel:

C= 2pi(r)

C= (2)(3.14)(60)

= 376.99



5. Area of the wheel:

A= pi(r)^2

A= (3.14)(60)^2

= 11309.73

　



6. Measure of a central angle in degrees:

360 / 32 = 11.25 degrees

7. Measure of a central angle in radians:

11.25 - pi/180

=11.25pi/180

reduce

= 0.19634954 radian

　


8. Arc length between two cars or compartments :

2pi r(x) / 360
2pi (60)(11.25) /360 = 11.78


9. Area of a sector between two cars or compartments : pi r^2(x) / 360
pi (60^2)(11.25) / 360 = 353.43