In Round County, all pasture land is formed by circles or partial circles connected together. For example, Pasture A is made from three half circles, as seen on this map:
- Compare Pasture A with Pasture B, pictured below.
- Which of the two pastures has a greater area? Explain (provide a convincing mathematical explanation).
- Each pasture requires fencing that follows the curve of the outside of the pasture. Which pasture requires more fencing--that is, which one has the larger perimeter? Explain (provide a convincing mathematical explanation).
- Pasture C is shown below.
- How much fencing does Pasture C require? Explain.
- How does the amount of fencing required for Pasture C compare to that required for Pastures A and B? Explain why this relationship exists.
- What is the area of Pasture C? Explain.
- Pasture D is shown below.
- Predict (before calculating) the amount of fencing needed for Pasture D. Explain how you made your prediction.
- Check your prediction by calculating how much fencing is required.
Pasture E is shown below.
- Describe two ways to compute the exact area of Pasture E. Explain each method.
- How much fencing does Pasture E require? Explain.