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Math Example--Area and Perimeter--Circular Area and Circumference: Example 17

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# Math Example--Area and Perimeter--Circular Area and Circumference: Example 17

## Topic

Geometry

## Description

This example presents two concentric circles with radii of 5 and 4 units, and a shaded sector with a central angle of 30 degrees. The task is to calculate the perimeter of the shaded region. The solution involves calculating arc lengths based on the central angle and adding straight-line segments between radii: Perimeter = (θ / 360) * (2 * π * r_{1} + 2 * π * r_{2}) + 2 * (r_{1} - r_{2}) = (30 / 360) * (2π * 5 + 2π * 4) + 2 * (5 - 4) = 3π / 2 + 2.

Calculating perimeters of complex shapes like sectors between concentric circles helps students develop problem-solving skills and spatial reasoning. This example combines concepts of arc length and linear distance, encouraging a more holistic understanding of geometric measurements.

Exposure to multi-step problems that involve both circular and linear elements prepares students for more advanced mathematical thinking. These examples foster the development of analytical skills within a geometric context, bridging the gap between different areas of mathematics.

**Teacher:** "Consider why we need to include both arc lengths and straight-line segments in this calculation. How does the central angle affect each part of the perimeter? Can you think of a real-world situation where calculating such a perimeter might be useful?"

For a complete collection of math examples related to Circular Area and Circumference click on this link: __Math Examples: Circular Area and Circumference Collection.__

Common Core Standards | CCSS.MATH.CONTENT.7.G.B.4 |
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Grade Range | 6 - 8 |

Curriculum Nodes |
Geometry• Circles• Area and Circumference |

Copyright Year | 2013 |

Keywords | area, circumference, circle |