PLEASE HELP ! 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?\

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.

my calculations:
Name of ferris wheel: Singapore Flyer
Diameter: 150 meters
Number of compartments: 28
Circumference of the wheel: 471 meters.
Area: 17,662.5 meters.
The central angle in degrees is 12.86
The central angle in radians: .224
Arc length: 16.8
Area of a sector: 630

The characteristics of similarity of circles is that all circles are similar

The result of the comparison  between the parameters of the original and the replica of the Ferris wheel are as follows;

i) The Ferris wheels are similar and represent similar circles,

The central angles of both Ferris wheels are equal

ii) The smaller Ferris wheel has a smaller arc length than the original Ferris wheel

iii) The equation of the replica of the Ferris wheel is x² + y² = 900

iv) Please find attached the image of the Ferris wheel

The reasons for the above values presented are correct are as follows;

Known;

The given parameters of the original Ferris wheel are;

The Ferris wheel name = Singapore Flyer

Wheel diameter = 150 m

Number of compartments = 28

Wheel circumference ≈ 471 m

Wheel area ≈ 17,662.5 m²

Central angle measure = 12.86°

Central angle measure in radians ≈ 0.224

The distance between two cars (arc length) = 16.8

Sector area of region between two cars = 630 m²

Strategy;

To show that the measure of angles in the similar circles are equal

The required parameter are;

The parameters of smaller replica of the Ferris wheel;

The diameter of the wheel, D = 60 meters

The location of the center = (0, 0)

Number of compartments = 28

Wheel circumference, C = π × D = π × 60 ≈  188.5 m

Wheel area ≈ π × D²/4 = π × (60 m)²/4 ≈ 2827.43 m²

Central angle measure = 360/28 ≈ 12.86°

Central angle measure in radians = 2×π/28 ≈ 0.224

The distance between two cars (arc length) = C/28 = 188.5/28 ≈ 6.73 m

Sector area of region between two cars = 2827.43 m²/28 ≈ 101 m²

i) The original and replica of the Ferris wheel are similar, therefore, the conclusion that can be drawn about the central angle is that they will be equal

ii) The arc length of the smaller Ferris wheel is less than the original Ferris wheel

iii) The general equation of a circle is (x - h)² + (y - k)² = r²

Where;

(h, k) = The center of the circle = (0, 0)

r = The radius of the circle of the Ferris wheel = D/2 = 60 m/2 = 30 m

Therefore, the equation of the smaller replica of the Ferris is presented as follows;

(x - 0)² + (y - 0)² = x² + y² = 30² = 900

The equation of the replica of the Ferris wheel is x² + y² = 900

iv) The drawing of the Ferris wheel created with MS Excel is attached

Learn more about Ferris wheel here;

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