In one rotation of the carousel, how much farther does Mai travel than Kiran?
Understand the Problem
The question is asking how much farther Mai travels compared to Kiran in one rotation of the carousel. Kiran rides on an inner ring with a radius of 9 feet, while Mai rides on the outer ring, which is 8 feet farther out. To solve it, we will calculate the circumferences of both rings and find the difference.
Answer
Mai travels $16\pi$ feet farther than Kiran.
Answer for screen readers
Mai travels $16\pi$ feet farther than Kiran in one rotation of the carousel.
Steps to Solve
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Calculate Kiran's Radius Kiran rides on the inner ring, which has a radius of 9 feet.
$$ R_K = 9 \text{ feet} $$
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Determine Mai's Radius Mai rides on the outer ring, which is 8 feet farther out than Kiran.
$$ R_M = R_K + 8 = 9 + 8 = 17 \text{ feet} $$
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Calculate Kiran's Circumference The formula for the circumference $C$ of a circle is given by:
$$ C = 2 \pi R $$
So for Kiran:
$$ C_K = 2 \pi R_K = 2 \pi (9) = 18\pi \text{ feet} $$
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Calculate Mai's Circumference Using the same circumference formula for Mai:
$$ C_M = 2 \pi R_M = 2 \pi (17) = 34\pi \text{ feet} $$
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Find the Difference in Distances Traveled To find out how much farther Mai travels than Kiran, subtract Kiran's circumference from Mai's circumference:
$$ \text{Difference} = C_M - C_K = 34\pi - 18\pi = 16\pi \text{ feet} $$
Mai travels $16\pi$ feet farther than Kiran in one rotation of the carousel.
More Information
The circumferences of circles relate directly to their radii, and this problem highlights how even a small increase in radius can lead to a significantly larger distance traveled in a circular path.
Tips
- Forgetting to add the additional 8 feet for Mai's radius.
- Confusing the formulas for calculating circumference.
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