A carnival ride is in the shape of a wheel with a radius of 15 feet. The wheel has 24 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit. (10 points)
Accepted Solution
A:
1) Given that there are 24 cars equally divided, each space between two adjacent cars is the 1 /24 of the total space.
2) Central angle of a sector between to adjacent cars:
=> divide the angle of the whole circle by 24 => 360° / 24 = 15°
3) arc length between two adjacent cars:
=> divide the total length of the circle by 24.
The total length of the circle is the circumference = 2π(radius) = 2π(15 feet)
total length = 94.25 feet
=> arc length = 94.25 feet / 24 = 3.93 feet
4) area of a sector between two adjacent cars:
=> divide the area of the circle by 24
area of the circle = π(radius)^2 = π(15 feet)^2 = 706.86 feet^2
=> area of the sector = 706.86 feet^2 / 24 = 29.45 feet^2