分类固体数字

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Mack is building a garden for his mother. He wants to put in pentagonal stones to decorate the area . In order to make the best arrangement, he needs to find the number of faces and edges in a pentagonal prism . How many faces and edges are there in a pentagonal prism?
::麦克正在为母亲建造花园。 他想在五角形石头中装饰这个区域。 为了做出最佳安排,他需要找到五角形棱镜中的脸和边缘。 五角形棱镜中有多少面和边缘?

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In this concept, you will learn how to classify by identifying faces, edges and vertices .
::在此概念中,您将学会如何通过识别面部、边缘和脊椎进行分类。

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Solid Figures
::实实数字

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Solid figures are shapes that exist in three-dimensional space . Unlike plane figures, which have only length and width, solid figures have length, width, and height . Let’s take a look at identifying solid figures.
::固态数字是三维空间中存在的形状。 与只有长度和宽度的平面数字不同,固态数字有长度、宽度和高度。 让我们来看看确定固态数字。

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Here are three different prisms . Each figure has two common congruent bases and these bases are hexagons, pentagons and triangles. The sides of each figure are made up of . You name these figures according to the base: a hexagonal prism, a pentagonal prism and a triangular prism . Notice that the key with prisms is that the sides are rectangles.
::这是三个不同的棱镜。 每个图有两个共同的相容基座, 这些基座是六边形、 五边形和三角形。 每个图的侧面由 。 您按底座命名这些数字: 六边形棱镜、 五边形棱镜和三角棱镜。 请注意, 棱镜的关键是两边是矩形 。

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Another type of is called a pyramid . A pyramid has a base and triangular sides that meet at a single vertex . You identify a pyramid according to its base.
::另一种类型被称为金字塔。金字塔有一个基边和三角边,在单一顶点相交。您根据金字塔的底部识别金字塔。

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Here are some pyramids.
::这里有一些金字塔。

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There are other solid figures too that have circles in them. See below a cylinder , a cone, and a sphere .
::还有其他有圆圈的可靠数字。请参看下面的圆筒、圆锥和球体。

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Solid figures have faces , edges and vertices . You can use the number of faces, edges and vertices to identify the solid figures. 
::固态数字有面、 边缘和顶点。 您可以使用面、 边缘和顶点的数量来识别固态数字 。

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A face is the flat side of a solid figure. Faces are in the form of plane shapes, such as triangles, rectangles, and pentagons. An edge is the place where two faces meet. Edges are straight; they cannot be curved. Vertices or a vertex is the point where edges meet.
::面部是固态图形的平面。 面部是平面形状的形式, 如三角形、 矩形和五角形。 边缘是两面相交的地方。 边缘是直的, 无法弯曲。 边缘或顶部是边缘相交的地方 。

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You can identify the three parts of a solid by looking at the following diagram .
::您可以通过查看下图来识别固体的三部分。

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Once you know how to identify the faces, edges and vertices of a solid, you can count them too.
::一旦你知道如何识别一个固体的面部、边缘和脊椎,你也可以计算它们。

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Let’s look at an example.
::让我们举个例子。

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How many faces, edges, and vertices does the figure below have?
::下图有多少面孔、边缘和脊椎?

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First, let’s count the faces. Remember, each face is a flat plane shape. In this figure, the bases, or top and bottom, are hexagons and the sides are all rectangles. There are six faces around the sides and two bases. This figure has eight faces in all.
::首先,让我们计数脸。 记住, 每张脸都是平平面形状。 在这张图中, 底部和上部都是六边形,两边都是矩形。 两边有6张面,两边有2个。 这个数字共有8张面。

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Next, let’s count the edges where each face meets another. There are six around the top hexagon where it meets each side, and six more around the bottom hexagon where it meets each side. And there are six more where each side meets another. This figure has 18 edges.
::接下来,让我们来计算每面相遇的边缘。 顶端六边有6个,每面相遇,下边有6个。 下边有6个,每面相遇。 下边有6个,每面相遇。 这个数字有18个边缘。

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Then, let’s find the vertices. Remember, a vertex is like a corner. This figure has six corners, or vertices, on the top and six on the bottom. This figure has twelve vertices in all.
::然后,让我们找到顶点。 记住,顶点就像一个角落。 这个数字在顶部有六个角,在底部有六个顶点。 这个数字共有12个顶点。

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You can count faces, edges and vertices of all the solids. This information can also help us to classify them. If you think about prisms and pyramids, you can think about the number of edges, faces and vertices.
::您可以计算所有固体的面、 边缘和顶点。 此信息也可以帮助我们分类它们。 如果您想一想棱镜和金字塔, 您可以考虑边缘、 面和顶点的数量 。

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However, if you think about a sphere, a cone and a cylinder, you will notice that faces, edges and vertices don’t apply to all of these.
::然而,如果你想到一个球体,一个锥体和一个圆柱, 你会注意到那些面孔,边缘和脊椎 并不适用于所有这些。

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Let’s look at a chart to help us classify solid figures according to their faces, edges and vertices.
::让我们看看一张图表, 帮助我们根据真实数字的面貌、边缘和脊椎进行分类。

Figure Name	Number of Faces	Number of Edges	Number of Vertices
sphere	0	0	0
cone	1	0	1
cylinder	2	0	0
triangle pyramid	4	6	4
square pyramid	5	8	5
prism	at least 5	at least 9	at least 6

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Let’s look at an example.
::让我们举个例子。

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Draw a triangular prism.
::绘制三角棱镜 。

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First, you know that a triangular prism has two bases shaped like triangles. To draw the triangular prism, let’s begin by drawing its base.
::首先,你知道三角棱晶有两个形状像三角形的基底。 要绘制三角棱晶,让我们从绘制其基底开始。

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Next, let’s draw the side that is facing toward the front. You know that a prism has rectangular sides that are all the same height. You also know that the bottom edge of the rectangular side connects to one edge of the base, so you can draw the rectangular face attached to the base.
::接下来,让我们把正向前方的侧面画出来。 你知道棱镜的长方形边面都具有相同的高度。 您也知道长方形边的底边缘连接到基底的边缘, 这样您就可以绘制与基底相连的长方形面 。

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Notice that the top face is exactly the same size and shape as the base, only it is connected to a top edge of the rectangular side. Imagine you could slide the base triangle up and put it on top of the rectangle .
::请注意, 顶部面的大小和形状与底部的大小和形状完全相同, 只有它被连接到矩形边的顶端。 想象一下您可以将底部三角形向上滑动, 并放在矩形的顶端 。

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It becomes easy to figure out how to draw this figure once you understand that the bases are triangles and as with any prism, the sides are rectangles. Connecting them together forms the solid figure.
::一旦你明白这些基座是三角形,就像任何棱镜一样,两边是矩形。把它们连接在一起就形成了坚固的图形。

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Examples
::实例

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Example 1
::例1

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Earlier, you were given a problem about  Mack’s stone pattern.
::先前,你对麦克的石块模式感到疑惑。

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Mack needs to know the number of faces and edges on a pentagonal prism in order to build a pattern of stone in the garden.
::麦克需要知道五角棱镜上 面孔和边缘的数量 才能在花园中建一个石头的图案

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First, you can use the fact that $\begin{array}{r}n+2\end{array}$  gives us the pattern for the number of faces in a prism. In this pattern, $\begin{array}{r}n\end{array}$  represents the number of sides in the base. The pentagon has five sides, so we know that $\begin{array}{r}n\end{array}$  is 5.
::首先,您可以使用 n+2 给我们的棱晶面数模式。 在这个模式中, n 代表基点的边数。 五角形有五个边, 所以我们知道 n 是 5 。

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::脸孔=n+2脸孔=7脸孔

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Next, draw a picture of a pentagonal prism.
::接下来,绘制一个五角形棱镜的图片。

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From the drawing, you can count the edges.
::从绘图中,你可以计算边缘。

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Faces: 7
::面孔:7

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Edges: 15
::边缘:15

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Vertices: 10
::顶点:10

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The answer is 7 faces, 15 edges, and 10 vertices.
::答案是7张脸,15个边缘,10个顶点。

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Example 2
::例2

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Sketch a cylinder.
::画一个圆柱子。

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First, remember that cylinders have two circular bases. Therefore you will need to draw a circular base which is the same as the circular top face.
::首先, 请记住圆柱体有两个圆形基体。 因此您需要绘制一个圆形基体, 与圆形顶部的圆形基体相同 。

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Next, add the front view. Cylinders do not have a side face. They are curved. Imagine holding up a cylinder and looking at it from the side. What would it look like? From the side, the cylinder would appear to have a rectangular face. This is a bit of an illusion, but you should sketch the cylinder as you would see it. Even though the side meets the base around the curve of the circle , you can draw a rectangle. But let’s show the top and bottom of the rectangular side with dashed lines so that you know there isn’t really a straight edge there.
::加入前方视图。 圆柱体没有侧面面面, 它们被弯曲了 。 想象一下将圆柱体举起并从侧面看一看。 它会是什么样子 ? 从侧面看, 圆柱体似乎有长方形面 。 这是一个幻觉, 但是您应该像您所看到的一样画出圆柱形。 尽管圆形的底部与圆形的曲线相近, 您也可以绘制矩形。 但是让我们用虚线显示矩形侧的顶部和底部, 以便您知道那里没有真正的直边 。

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There aren’t any vertices to connect between the top and bottom faces since they are round, so you’re done.
::上面和下面的面孔之间没有任何顶点可以连接,

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Example 3
::例3

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Name the figure below and name the number of vertices, faces, and edges.
::列出下方的图表,并列出顶点、面部和边缘的数量。

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First, name the figure.
::首先,请说出数字。

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Rectangular Prism
::矩形棱柱

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Next, find the number of vertices, faces, and edges.
::下一步,找到脊椎、面孔和边缘的数目。

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Vertices: 8
::顶点: 8

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Faces: 6
::面孔:6

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Edges: 12
::边缘:12

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The answer is there are 8 vertices, 6 faces, and 12 edges.
::答案是,有8个顶端,6个面孔,12个边缘。

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Example 4
::例4

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Name the figure below and name the number of vertices, faces, and edges.
::列出下方的图表,并列出顶点、面部和边缘的数量。

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First, name the figure.
::首先,请说出数字。

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Hexagonal Prism
::六边形棱柱

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Next, find the number of vertices, faces, and edges.
::下一步,找到脊椎、面孔和边缘的数目。

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Vertices: 12
::顶点:12

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Faces: 8
::面孔:8

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Edges: 18
::边缘:18

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The answer is there are 12 vertices, 8 faces, and 18 edges.
::答案是,有12个脊椎,8个面孔,18个边缘。

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Example 5
::例5

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Name the figure below and name the number of vertices, faces, and edges.
::列出下方的图表,并列出顶点、面部和边缘的数量。

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First, name the figure.
::首先,请说出数字。

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Cone
::锥体

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Next, find the number of vertices, faces, and edges.
::下一步,找到脊椎、面孔和边缘的数目。

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Vertices: 0
::顶点: 0

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Faces: 1
::面孔:1

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Edges: 0
::边缘:0

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The answer is there are 0 vertices, 1 faces, and 0 edges.
::答案是,有0个顶部,1个面孔和0个边缘。

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Review
::回顾

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Answer the following questions about each solid figure.
::回答以下关于每一可靠数字的问题。

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1. What is the name of this figure?
::1. 这个数字叫什么名字?

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2. How many faces does it have?
::2. 它有多少面孔?

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3. How many vertices does it have?
::3. 有多少顶峰?

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4. How many edges does it have?
::4. 它有多少边缘?

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5. What is the name of this figure?
::5. 这个数字叫什么名字?

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6. How many faces does it have?
::6. 它有多少面孔?

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7. How many edges does it have?
::7. 它有多少边缘?

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8. How many vertices does it have?
::8. 有多少顶峰?

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9. What is the name of this figure?
::9. 这个数字叫什么名字?

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10. How many faces, edges and vertices does it have?
::10. 有多少面孔、边缘和脊椎?

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11. What is the name of this figure?
::11. 这个数字叫什么名字?

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12. How many faces does it have?
::12. 它有多少面孔?

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13. How many edges does it have?
::13. 它有多少边缘?

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14. How many vertices does it have?
::14. 有多少顶峰?

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15. A figure has one circular face, no edges, and no vertices. What kind of figure is it?
::15. 数字有一个圆形面,没有边缘,没有脊椎,是什么样的数字?

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16. A figure has one pair of parallel sides that are circular. What kind of figure is it?
::16. 数字有一个平行的两面,是圆形的,是什么样的数字?

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17. Sketch a cone.
::17. 绘制锥形。

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18. Sketch a pentagonal prism.
::18. 绘制五角形棱镜。

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Review (Answers)
::回顾(答复)

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Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

 

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Resources
::资源