Question

A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 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)

Answer 1

Centre angle will be 360° as its totally a circle.

• radius=r=25ft

Angle between two cars=360/20=18°

• Arc length=L

`\\ \sf\longmapsto L=(\theta)/(360)(2\pi r)`

`\\ \sf\longmapsto L=(18)/(360)(2\pi(25))`

`\\ \sf\longmapsto L=(1)/(20)(50\pi)`

`\\ \sf\longmapsto L=2.5\pi ft`

Now

Area be A

`\\ \sf\longmapsto A=(1)/(2)Lr^2`

`\\ \sf\longmapsto A=(1)/(2)(2.5\pi)(25)^2`

`\\ \sf\longmapsto A=625(2.5)\pi(1)/(2)`

`\\ \sf\longmapsto A=1562.5\pi/2`

`\\ \sf\longmapsto A=781\pi ft^2=`