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)

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.