Math Problem Statement
Solution
The image shows an oval track with two straight sections and two semicircles at each end. The dimensions provided are:
- Length of the straight section = 300 feet
- Diameter of each semicircle = 140 feet
To calculate the approximate distance around the track, we need to find the total perimeter. The perimeter consists of:
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Two straight sections: Each straight section is 300 feet long, so the total length of the straight sections is:
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Two semicircles: The diameter of each semicircle is 140 feet, so the radius is: The circumference of a full circle is , but since we have two semicircles (which together form a full circle), the total length of the two semicircles is: Approximating as 3.1416, the length of the two semicircles is:
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Total distance around the track: Adding the lengths of the straight sections and the semicircles, we get:
So, the approximate distance around the track is 1039.6 feet, or about 1040 feet.
Would you like further details on this calculation or clarification?
Here are 5 related questions to expand on this:
- How would the perimeter change if the straight sections were longer?
- What is the area enclosed by the oval track?
- How would you calculate the perimeter if the track was elliptical instead of semicircular at the ends?
- Can you calculate the distance around the track for multiple laps, such as 3 or 5 laps?
- How would the distance change if the semicircles had a different radius?
Tip: For shapes involving circular sections, always consider whether you're dealing with a full circle or just a portion of it, and adjust your formula accordingly.
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Math Problem Analysis
Mathematical Concepts
Geometry
Perimeter of composite shapes
Circumference of circles
Formulas
Perimeter of a semicircle = π * radius
Perimeter of an oval = sum of straight sections + circumference of semicircles
Theorems
Circumference of a circle theorem
Suitable Grade Level
Grades 6-8
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