a ferris wheel has a diameter of 42 feet. it rotates 3 times per minute. approximately how far will a passenger travel during a 5-minute ride?

132 feet
659 feet
1,978 feet
3,956 feet

Question

a ferris wheel has a diameter of 42 feet. it rotates 3 times per minute. approximately how far will a passenger travel during a 5-minute ride?

132 feet
659 feet
1,978 feet
3,956 feet

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circumference Formula" ], "new_concepts": [], "current_concepts": [ "Circumference Formula", "Rotational Rates" ] } ## Calculate the circumference of the Ferris wheel $$ \begin{aligned} d &= 42\text{ feet} \ C &= \pi d = 42\pi \approx 131.947\text{ feet} \end{aligned} $$ ## Determine the total number of rotations $$ \begin{aligned} \text{Rotations per minute} &= 3 \ \text{Total time} &= 5\text{ minutes} \ \text{Total rotations} &= 3 \times 5 = 15 \end{aligned} $$ ## Calculate the total distance traveled $$ \begin{aligned} \text{Total distance} &= 15 \times C \ &= 15 \times 42\pi \ &= 630\pi \ &\approx 1979.2\text{ feet} \end{aligned} $$

132 feet

659 feet

1,978 feet

3,956 feet

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circumference Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the circumference of the Ferris wheel

Determine the total number of rotations

Calculate the total distance traveled

Answer: