棱柱就是一种立体几何图形,有着全等的两个底面,所有侧面平行。一个棱柱以其底边形状命名,因此三角形为底边的棱柱就是三棱柱。要找出体积,需要知道底边面积乘上高度——算底面积可能比较麻烦。以下介绍如何计算多种棱柱体积的方法。
步骤
方法 1 的 5:
计算三棱柱体积
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1
写出三棱柱体积公式。 即V = 1/2 x 长度 x宽度x高度 ,我们换个角度,即V = 底面面积x 高度 。你可以通过算三角形面积的方法得到底面面积,也就是俗称的“底乘高的1/2”。
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2
得出底面面积。 要计算体积,需要找出底面面积。底面三角形的高乘以对应边长再除以2即可。
例如底面高5 cm,对应底边是 4 cm, 1/2 x 5 cm x 4 cm = 10 cm2 得出面积。
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3
找出棱柱的高。 这里假设为7 cm。
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4
把底面面积乘以高即可。 乘起来以后就得到三棱柱的体积了。
例如:10 cm2 x 7 cm = 70 cm3
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5
用立方单位来表示体积。 要用立方单位才能表示出三维的体积。最终答案是70 cm3 。
方法 2 的 5:
计算正方体的体积
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1
写出正方体体积公式V = 边长3 。 正方体就是所有边长都相等的棱柱。
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2
找出一条边长。 所有的都一样,找一条就够了。
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3
求出立方。 将该数对自己乘两次即可。"a" 的立方就表示为 "a x a x a" 。因为所有立方体的边长相等,你就不用找底面积和高了。任两边相乘都可以得到底面积,任意边都相当于高。你也可以把这个想成是长宽高三者相乘。
例如 (3 cm) 3 = 3 cm * 3 cm * 3 cm = 27 cm3
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4
最终答案用立方单位表示:27 cm3 。
方法 3 的 5:
计算长方体体积
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1
写出长方体体积公式V = 长度 * 宽度 * 高度 ,长方体就是底面为长方形的棱柱。
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2
找出长。 长就是底面较长的边,可以在上底面找,也可以在下底面找。
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3
找出宽。 宽就是底面较短的边,可以在上底面找,也可以在下底面找。
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4
找出高。 高就是竖直的那条边。你可以想象成底面上突出的一根边,想成三维形状的。
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5
将长度、宽度、高度乘起来。 你可以任意顺序乘,用这个方法,本质上你已经找到底面积了( 10 x 8) ,然后乘以高度 5,不过这种棱柱可以任意顺序乘边长求得体积。
如: 10 cm * 8 cm * 5 cm = 400 cm3
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6
用立方单位表示答案: 400 cm3 。
方法 4 的 5:
计算梯形体体积
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1
写下公式计算梯形体体积: V = [1/2 x (底边1 + 底边2) x高度] x 棱柱高 ,你要看出这个公式的前一部分是用来找出底面积,然后继续下一步。
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2
得到底面积大小。 你可以把两个底边长和底面高代入公式。
例如:底边1 = 8 cm 底边2 = 6 cm 高度= 10 cm
如: 1/2 x (6 + 8) x 10 = 1/2 x 14 cm x 10 cm = 80 cm2
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3
找出棱柱高度,假设为12 cm。
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4
将底面积乘以高。 得到梯形体的体积。
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5用立方单位来表示,这样得到960 cm3
方法
5
方法 5 的 5:
计算正五棱柱体积
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1
写出正五棱柱体积公式:V = [1/2 x 5 x 边长 x 边心距] x 棱柱高 1/2 ,前一部分是用来算正五边形底面积的,其实可以想成计算五个三角形的总面积。 边长就是这些三角形的底边长,你需要除以2,得到三角形的面积,然后乘以5,因为一个正五边形里总共有5个三角形
要了解更多关于边心距的知识,可以查阅wikiHow中计算边心距的文章。
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2
找出五边形底面的面积。 我们假设底边长6 cm,边心距 7 cm ,代入公式:
A = 1/2 x 5 x 边长 x 边心距
A = 1/2 x 5 x 6 cm x 7 cm = 105 cm2
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3
找出棱柱高度。 假设为10 cm
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4
将面积乘以高,即105 cm2 乘以 10 cm得到标准五棱柱体积。
105 cm2 x 10 cm = 1050 cm3
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5用立方单位表示答案: 1050 cm3
小提示
不要把底边和底面弄混了。底面积表示二维的平面,是棱锥的底面(上底面和下底面),而底面有自己的底——底边,是一维的线段,作为计算底面积的一条边来用。