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The Swimming Area Problem: Grade 8 Version
You and two of your friends have summer jobs as lifeguards at the waterfront. Your boss gives each of you 100 m of rope to use to enclose three different swimming areas surrounding a floating platform. One of the swimming areas will be a square, one will be an equilateral triangle, and one will be circular.
Problem 1: Which of the shapes will enclose the largest area for the swimmers?
Recall the formulas for Circumference, and Area
C = 3.14(d) A = 3.14(r2) A = lw A = lw / 2
Hypothesis: Make a hypothesis about which shape will give the largest swimming area given 100 m of rope.
Data Collection:
Calculate the area of the three different shapes.
Record your results in a chart.
Problem 2: What will happen to the size of the swimming area if the length of the
rope is doubled? tripled? quadrupled?
Hypothesis: Make a hypothesis about what will happen to the size of the swimming
areas.
Data Collection:
Calculate the new areas for the three different shapes.
Record your results in a chart.
Construct a triple line graph using the data from the previous chart. Use length and area as your axis. Length is on the horizontal axis and area is on the vertical axis. Be sure that the graph includes a title, a legend, and that the axis are labeled.
Conclusion:
Based on your graph, what happens to the area of each shape as the length of rope increases?.
EXTENSION ACTIVITY:
Choose the shape that yielded the largest area using the 100 m rope. Now you want to enclose a swimming area that uses the beach as one of the sides. What is the size of the new swimming area?