Question

A giant wheel has a radius of 14 ft. To the nearest tenth of a foot, what distance does the giant wheel cover when it rotates through an angle of 96∘?

Answer 1

General Idea:

Length of a sector is given by the below equation:

`Length \; \; of\;\; Sector \;\; of\; Circle = (\theta )/(360) \cdot 2 \cdot \pi \cdot r\\ where \; \; \theta \;is\; in \;degrees \; and \; r\; is\; radius`

Applying the concept:

Given
`\theta = 96^(\circ)` and
`r=14ft`

Substituting the above details in the formula, we get...

`Length\; \; of\;\;sector\;\;of\;\;circle=(\96)/(360) \cdot 2 \cdot \pi \cdot 14\approx 23.5\; feet`\

Conclusion:

The Distance that the giant wheel cover when it rotates through an angle of 96∘ is 23.5 feet.