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An amusement park has two merry-go-rounds. The first merry-go-round has a platform with a diameter of 13 meters and the second merry-go-round has a platform with a radius of 9.5 meters. How much larger is the area of the larger merry-go-round’s platform compared to the area of the smaller merry-go-round’s platform? Round to the nearest whole number. Show your work. (Use Pi = 3.14)

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Edufirst

Answer:

  • The larger merry-go-round's platform is   151m²   larger than the smaller merry-go-round's platform.

Explanation:

The area of a round shape is equal to the area of a circle.

The formula for the area of a circle is:

  • Area = π × radius²

Then, use that formula for each merry-go-round.

1. First merry-go-round

  • diameter = 13m
  • radius = diameter / 2 = 13m / 2 = 6.5m
  • area = π (6.5m)² = 3.14 × (6.5m)² = 132.665m²

2. Second merry-go-round

  • radius =9.5m
  • area = π (9.5m)² = 3.14 × (9.5m)² = 283.385‬m²

3. Difference of the areas

  • Larger area - smaller area = 283.385m² - 132.665m² = 150.72m²

  • Round to the nearest whole number: 151m².

Hence, the larger merry-go-round's platform is 151m² larger than the smaller merry-go-round's platform.

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