| There is a circular pond in front of the school. | ||
| The pond is 20 feet in diameter. | ||
| The school board wants to build a sidewalk around the pond. | ||
| They want to make the sidewalk 3 feet wide. | ||
| What is the area of the sidewalk? | ||
| OK, so the pond has a diameter of 20 feet. | ||
| A diameter is the distance | ||
| from one side of a circle to the other. | ||
| A radius is the distance | ||
| from the center of the circle to the edge. | ||
| The radius is one half of the diameter.. | ||
| So the radius of the pond is 10. | ||
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| The area of the circle is equal to pi (3.14159 ...) | ||
| times the radius squared. | ||
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Area = pr2 |
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| The area of the pond is ... | ||
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Area = (3.1416)(102) |
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Area = 314.2 square feet |
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| The sidewalk is to be 3 feet wide. | ||
| The distance from the center of the circle | ||
| to the outside of the sidewalk is 10 + 3 = 13 feet. | ||
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| If we didn't have a pond at all, | ||
| but just a round slab of concrete with a radius of 13 | ||
| the area would be ... | ||
|
Area = p(13)2 |
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|
Area = p(169) |
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Area = 530.9 square feet |
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| But we DO have a pond in the middle. | ||
| The area of the pond is 314.2 square feet. | ||
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| So the area of the 3 foot wide walk, | ||
| is the area of the 13 foot radius concrete disk | ||
| minus the area of the 10 foot radius pond | ||
| in the middle of it. | ||
| Area of walk = 530.9 sq. ft. - 314.2 sq. ft. | ||
| Area of walk = 216.7 sq ft. | ||
| So this is the strategy you use with the | ||
| "border around the edge" problems. | ||
| Find the area of the surface to the edge of the border | ||
| Subtract the area of the thing in the middle. | ||
|
copyright 2005 Bruce Kirkpatrick |
