Math Problem Statement
for conducting a race of 400 m and for having 6 lanes of width 1m the area of the circular field required will be
Solution
To determine the area of a circular field required for a 400-meter race with 6 lanes, each of width 1 meter, we need to calculate the area of the field including the track and the inner circular area.
Understanding the Problem
- Track Length: The total length of the race is 400 meters. In a circular track, this is the perimeter of the innermost lane.
- Lanes: There are 6 lanes, each with a width of 1 meter.
- Radius of the Inner Lane (r): Let's assume the radius of the innermost lane is .
Step-by-Step Solution
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Perimeter of the Innermost Lane:
The perimeter (circumference) of the innermost lane is 400 meters:
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Outer Radius of the Track:
Since there are 6 lanes, each 1 meter wide, the outermost lane will be at a distance of 6 meters from the innermost lane. Therefore, the outer radius is:
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Area of the Circular Field:
The required area is the area of the outer circle with radius :
Let's compute this area.The area of the circular field required for a 400-meter race with 6 lanes, each 1 meter wide, is approximately 15,245.49 square meters.
Would you like more details on this calculation or have any other questions?
Related Questions:
- How do different lane widths affect the total area of a track?
- What is the formula for calculating the area of a circular track with multiple lanes?
- How can the length of each lane be determined in a circular race track?
- How does the shape of the track affect the running dynamics of the race?
- What are the standard dimensions for athletic tracks in international competitions?
Tip: When designing a race track, remember to consider not only the total area but also the safety zones and space for spectators.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circular Track Calculation
Formulas
Perimeter of a circle: 2πr
Area of a circle: πR^2
Theorems
Circumference of a circle
Area of a circle
Suitable Grade Level
Grades 9-12
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