The seattle great wheel is an illustration of sectors, arcs, circumference and area of circles
The circumference of the wheel
The diameter is given as:
d = 175 feet
The circumference (C) is calculated as:
C = πd
This gives
C = 3.14 * 175
C = 549.5 feet
Hence, the circumference of the wheel is 549.5 feet
The area of the wheel
This is calculated as:
A = π(d/2)^2
This gives
A = 3.14 * (175/2)^2
A = 24040.625
Hence, the area of the wheel is 24040.625 square feet
The central angle (degrees)
This is calculated as:
θ = 360/n
Where n is the number of capsules
So, we have:
θ = 360/42
This gives
θ = 8.57 degrees
Hence, the central angle of the wheel in degrees is 8.57
The central angle (radians)
This is calculated as:
Radians = Degrees × π/180
So, we have:
θ = 360/42 * π/180
This gives
θ = π/21 rad
Hence, the central angle of the wheel in radians is π/21 rad
Arc length between two capsules
This is calculated as:
L = θ * d/2
So, we have:
L = π/21 * 175/2
This gives
L = 175π/42
Hence, the arc length between two capsules is 175π/42
Area of sector between two capsules
This is calculated as:
A = 0.5 * (d/2)^2 * θ
So, we have:
A = 0.5 * (175/2)^2 * π/21
This gives
A = 168π
Hence, the area of sector between two capsules is 168π
Read more about sector areas and arc lengths at:
https://brainly.com/question/4115882
