Calculate Maximum Circles from a Rectangle: Geometry Problem

Math Problem Statement

长12cm宽7cm的纸，要剪半径1cm的圆，最多能剪多少个？

Solution

要确定最多可以剪多少个半径为1 cm的圆形，我们可以先计算每个圆的面积，然后用纸的总面积除以圆的面积。纸张的面积为长 × 宽，即 $12 \times 7 = 84 \, \text{cm}^2$ 。每个圆的面积为 $\pi \times (1)^2 = \pi \, \text{cm}^2$ 。然后，计算纸张总面积除以单个圆的面积，得到能剪的圆的最大数量。

由于圆形之间需要有空间来剪切，实际上能剪的数量会少一些，具体数量取决于圆的排列方式。

你想知道哪种排列方式（如矩形排列或蜂窝排列）能剪更多的圆吗？

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Circle Packing

Formulas

Area of a rectangle = length × width
Area of a circle = π × radius²

Theorems

Circle packing efficiency

Suitable Grade Level

Grades 6-8

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