Math Problem Statement
Pack the circles with diameter equal to 24 inches using square and hexagon.
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Circle Packing
Hexagonal Grid
Square Grid
Area Calculation
Formulas
Area of circle: A = π * (diameter / 2)^2
Area of square: A = side^2
Area of equilateral triangle: A = (sqrt(3) / 4) * side^2
Packing density for square grid: η = (π / 4)
Packing density for hexagonal grid: η = (π / (2 * sqrt(3)))
Theorems
Circle packing density
Hexagonal packing theorem
Suitable Grade Level
Grades 10-12
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