Question

A highway is going to be built around a city. The highway will be in the shape of a perfect circle, and its total length will be 251.2 kilometers. A nearby bus stop will have a billboard with a map of the bus routes along the highway. The map is drawn to a scale of 1:7,500. Calculate the area that is surrounded by the highway on the billboard map. Round the answer to the nearest hundredth of a square meter.

Answer 1

Answer:

The area that is surrounded by the highway on the billboard is approximately 89.34 square meters

Step-by-step explanation:

The given parameters are;

The length of the circle shaped highway = 251.2 km

The scale of the map of the bus routes along the highway = 1:7,500

The circumference of a circle, C = 2·π·r = The length of the perimeter of the circle

Therefore, we have;

The circumference of the highway = The length of the circle shaped highway = 251.2 km

The circumference of the highway, C = 251.2 km = 2·π·r

The radius of the circular highway path, r = 251.2 km/(2·π) ≈ 39.994217 km

The area of a circle, A = π·r².

The area of the highway = π·r² = π × (39.994217 km)² ≈ 5,025.09492434 km.²

Given that the scale of the map = 1:7,500. we have;

The scale of the area = (1:7,500)² = (1:56,250,000)

The size of the drawing, 5,025.09492434 km.²/(56,250,000) = 0.00008933502 km² = 89.33502 m.²

Therefore, the area that is surrounded by the highway on the billboard, rounded to the nearest hundredth of a square meter ≈ 89.34 m.²