一个立方体有多少个面、边和顶点?
测量是数学的一个分支,处理各种可用几何图形及其相关参数的研究,例如面积、长度、体积、侧表面积、表面积等。
立方体
立方体可以以方形棱柱的形式可视化。这是因为立方体的面是正方形的,本质上也是柏拉图式的。立方体的面也称为平面。
多维数据集的属性
- 所有的面都是正方形的,这意味着长、宽、高都是一样的。
- 任何两个面或曲面之间的角度都等于 90°。
- 相对的平面彼此平行。
- 相对的边缘彼此平行。
- 每个面与四个面形成交集。
- 每个顶点与三个面和三个边相交。
立方体的顶点
任何图形的顶点是两条或多条线段形成交点的点。它可以被认为是一个角落。一个立方体有 8 个顶点。
立方体的边缘
任何几何图形中的边都可以被认为是任意两个面形成交点的线段。它们构成了 3D 形状的骨架。它形成将一个顶点(角点)连接到另一个顶点的边界。一个立方体有 12 条边。
立方体的面
任何几何图形的面都是固体物体的各个平面。一个立方体有 6 个面。
立方体的公式
- 立方体的表面积 = 6a 2平方单位
其中,“a”是立方体的边
- 立方体的体积 = 一个3立方单位
其中,“a”是立方体的边
示例问题
问题 1. 如果立方体的边长为 6 厘米,求它的表面积?
解决方案:
Here we need to find the surface area of the cube.
Given:
Side of the cube = 6 cm
As we know that
Surface area of the cube = 6 × side × side
Surface area of the cube = 6 × side2
Surface area of the cube = 6 × 62
Surface area of the cube = 216 cm2
Therefore,
Surface area of the cube is 216 cm2.
问题 2. 如果立方体的边长为 4 m 2 ,求它的体积?
解决方案:
Here we need to find the volume of the cube
Given:
Side of the cube = 4 m2
As we know that
Volume of the cube = Side × Side × Side
Volume of the cube = Side3
Volume of the cube = 43
Volume of the cube = 4 × 4 × 4
Volume of the cube = 64 m3
Therefore,
Volume of the cube is 64 m3.
问题 3. 找出边长为 16 m 的大立方体在边长为 4 m 的小立方体中能拼出多少个小立方体?
解决方案:
Here we need to find out how many small cubes can be made out of one big cube.
As we know that
Volume of cube = Side3
Volume of big cube = Side × Side × Side
Volume of big cube = 16 × 16 × 16
Volume of big cube = 163
Volume of big cube = 4096 m3
Further,
Volume of small cube = Side × Side × Side
Volume of small cube = 4 × 4 × 4
Volume of small cube = 43
Volume of small cube = 64 m3
Now,
Number of small cubes that can be made from the big cubes = Volume of big cube/Volume of small cube
Number of small cubes = 4096/64
Number of small cubes = 64
Therefore,
64 small cubes will be made out of the big cube.
问题 4. 如果立方体的表面积是 486 m 2 。然后求立方体的体积?
解决方案:
Here we need to find the volume of the cube from a given surface area
Given:
Surface area of the cube = 486 m2
As we know that
Surface area of the cube = 6 × Side2
486 = 6 × Side2
Side2 = 486/6
Side2 = 81
Side = √81
Side = 9 m
Now,
Volume of cube = Side3
Volume of cube = 93
Volume of cube = 9 × 9 × 9
Volume of cube = 729 m3
Therefore,
Volume of the cube is 729 m3.