To find out how many revolutions the Ferris wheel makes during a ride of 450 yards, we first need to convert the diameter of the Ferris wheel into its circumference and then determine how many times that circumference fits into 450 yards.
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Calculate the radius: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{65 \text{ feet}}{2} = 32.5 \text{ feet} \]
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Calculate the circumference using the formula \( C = 2 \pi r \): \[ C = 2 \pi (32.5) \approx 2 \times 3.14 \times 32.5 \approx 204.2 \text{ feet} \]
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Convert 450 yards to feet (since there are 3 feet in a yard): \[ 450 \text{ yards} \times 3 \text{ feet/yard} = 1350 \text{ feet} \]
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Now, calculate the number of revolutions by dividing the total distance traveled by the circumference of the Ferris wheel: \[ \text{Number of revolutions} = \frac{\text{Distance traveled}}{\text{Circumference}} = \frac{1350 \text{ feet}}{204.2 \text{ feet}} \approx 6.61 \]
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Rounding to the nearest whole number, the number of revolutions is: \[ \approx 7 \]
Thus, the Ferris wheel makes approximately 7 revolutions.