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
Packing Efficiency
Circle Arrangements
Formulas
Area of a circle: A_circle = πr²
Square packing area: A_square = diameter²
Hexagonal packing area: A_hexagon = (3√3/2) × side²
Packing efficiency (square): π/4 ≈ 0.785
Packing efficiency (hexagonal): ≈ 0.9069
Theorems
Circle Packing Theorem
Hexagonal Lattice Packing
Suitable Grade Level
Grades 9-12
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