“学习数学对于参加农业生产是否用得上?”这个存在已久的老问题,是数学教学长期脱离生产斗争的具体反映,我们教师必须引起重视。下面介绍一些在修堤筑路中所遇到的土方计算问题,这些问题是与几何教学有着密切的联系。 (一) 计划修一条长50m的拦河坝,横断面是梯形,坝顶宽2m,坝高5m,迎水坡面与地面所成的角为28°,背水坡面与地面所成的角为36°。那么修此坝需多少方土?如果每个劳动力每天的工作量按3方来计算,需要多少个工才能完成? 解.如图1,可按拟柱体计算,我们有公式 V_(拟柱)=1/6h(Q_1+Q_2+4Q_0) 上底面积Q_1=长×宽=2×50=100(m~2), 又断面梯形下底=5ctg28°+2++5ctg36°≈18.3(m), ∴下底面积Q_2=长×宽=50×18.3=915(m~2), 中断面面积Q_0=长×宽(梯形中位线)= “The question of whether mathematics can be used to participate in agricultural production?” This long-standing old problem is a concrete reflection of the long-term struggle for mathematics teaching out of production. Our teachers must pay attention to it. Here are some of the earthwork calculations encountered in the construction of embankments and roads. These issues are closely related to geometry teaching. (i) Plan to build a 50m-long barrage with a trapezoidal cross-section, a 2m-wide crest, a 5m-high dam, an angle of 28° between the surface of the floodplain and the ground, and an angle of 36 between the backwater slope and the ground. °. So how much work is needed to repair this dam? If each worker’s daily workload is calculated on the basis of 3 parties, how many workers will be required to complete the solution? Figure 1. Can be calculated on a quasi-column basis. We have the formula V_(Quasi-column) ) = 1/6h (Q_1+Q_2+4Q_0) Upper end area Q_1=length×width=2×50=100(m~2), and the lower trapezoidal lower section=5ctg28°+2++5ctg36°≈18.3(m) ), Subgingival floor area Q_2=length×width=50×18.3=915(m~2), middle section area Q_0=length×width (trapezoidal median line)=