Question

3. A camival 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 calculationsto receive credit.

Answer 1

Central angle (in green): As the wheel has 20 cars divide 360º into 20 to find the central angle:

`\alpha=(360º)/(20)=18º`

Arc length (in blue):

`\begin{gathered} Al=(\alpha)/(360º)\cdot2\pi r \\ \\ Al=(18º)/(360º)\cdot2\pi\cdot25ft \\ \\ Al=(1)/(20)\cdot2\pi\cdot25ft \\ \\ Al=(50)/(20)\pi ft \\ \\ Al=(5)/(2)\pi ft \\ \\ Al=7.85ft \end{gathered}`

Area of the sector:

`\begin{gathered} As=(\alpha)/(360º)\cdot\pi\cdot r^2 \\ \\ As=(18º)/(360º)\cdot\pi\cdot(25ft)^2 \\ \\ As=(1)/(20)\cdot\pi\cdot625ft^2 \\ \\ As=(625)/(20)\pi ft^2 \\ \\ As=98.17ft^2 \end{gathered}`Then, the central angle is 18º, the arc length is 7.85 feet and the area of a sector is 98.17 square feet