Question

A carnival ride is in the shape of a wheel with a radius of 20 feet. The wheel has 16 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.

Answer 1

Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.

The total central angle around the wheel is 2π.

Therefore the central angle between two cars is

(2π)/16 = π/8 = 0.39 radians (nearest hundredth)

The arc length between two cars is

s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)

The area of a sector formed by two cars is

(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)

Answers: (to the nearest hundredth)

Between two cars,

Central angle = 0.39 radians (or 71.4°)

Arc length = 7.85 ft

Area of a sector = 78.54 ft²

Answer 2

Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.

The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)

The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)

The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)

Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²