数学题:将圆柱体加工成体积最大的长方体
- 时间:2020-06-09 15:19:31
- 分类:数学世界
- 阅读:158 次
数学题:将一个底面周长25.12分米,高5分米的圆柱形木料,加工成体积最大的长方体,求长方体木料体积。
数学题解答:先画图,长方体的高应等于圆柱体的高。若想长方体的体积最大,则长方体的底面应为正方形,且四个角应分别与圆相接触,即长方体的底面,是圆柱底面内的最大正方形。

接下来是计算,先算出底面的直径:
25.12 ÷ 3.14 =8(分米)
再算出底面半径:8 ÷ 2 = 4(分米)
再算出正方形的面积(当成两个大三角形来算):8×4÷2×2=32(平方分米)
最大的长方体的体积:32×5=160(立方分米)
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