宽2·2米,长12米的钢板,割直径1·6米的圆,最多能割几块?

宽2·2米,长12米的钢板,割直径1·6米的圆,最多能割几块?
2025年03月15日 11:57
有2个网友回答
网友(1):

能割8块
为了省材料,不妨设想为横放12米长钢板,从最靠近左上角处切第一个1.6米直径的圆,然后再最靠近剩余材料左下角切第2个圆,再左上、左下依次切下去。
作图可以看出当切出前2块圆板时,横向用掉的钢板长度小于(1.6*2=3.2)米,省下的横向部分长度为1.6-(1.6*1.6-(2.2-1.6)*(2.2-1.6))^(1/2)=0.11676米
设可切n块,从第2块开始,每增加一块,就多节省一段0.11676米,所以有
1.6*n-0.11676*(n-1)不大于12,计算可得n小于等于8.011679,由n为整数,所以n=8.

网友(2):

2.2÷1.6=1行............0.6米
12÷1.6=7列............0.8米
7X1=7块
答:割直径1.6米的圆,最多能割7块。

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