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  • 实实数净额

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    Michael and Amy bought Christmas gifts for their family.  The mall customer service center provided two types of boxes, but they're not sure on the final shape.  The boxes provided were in a flat stack for construction at home.  Michael and Amy need to figure out the shapes of the boxes when they are constructed so they know which gifts will fit in which boxes.  
    ::Michael 和 Amy 为他们的家人买了圣诞礼物。 商场客户服务中心提供了两种类型的箱子, 但它们在最后的形状上并不确定。 提供的箱子放在一个平板堆里, 供在家里建造。 Michael 和 Amy 需要弄清楚盒子的形状, 以便他们知道哪些礼物适合放在哪个盒子里 。

    In this concept, you will learn how to identify the 3-dimensional figure that a represents.
    ::在这个概念中,你将学会如何识别一个代表的三维数字。

    Nets of Solid Figures
    ::实实数净额

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    If you look at the above, you can see the parts of the figures that are toward you; however, you cannot see the parts that are on the backside and underneath or above.  If you want to see the entire figure, then you need to draw a representation of the figure that is two-dimensional, or planar.  You can think of this as unfolding or taking apart the solid so that you can see all of the parts.
    ::如果您看上面, 您可以看到数字中面向您的部分; 但是, 您看不到后面和下面或上面的部分。 如果您想要看到整张图, 那么您需要绘制一个二维或平面的图示。 您可以将此视为正在展开或分离的固态, 以便您能够看到所有部分 。

    Look back at the three figures. The first one is a rectangular prism . If you want to draw this as a two-dimensional figure, then you have to think about all of the parts of the rectangular prism.  There are four edges of the base of a rectangular prism, so you know that there are six faces.
    ::回顾这三个数字。 第一个是长方形棱柱。 如果您想将此画成二维图, 那么您就必须考虑长方形棱柱的所有部分。 长方形棱柱底部有四个边缘, 所以您知道有六个面孔 。

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    Look at how this box has been unfolded. You can see the pattern that it makes.  If you picture it in your mind, you can see how you could fold up the box again. The edges form the lines and you fold it along the dotted lines to create a rectangular prism once again.
    ::查看这个框是如何展开的 。 您可以看到它产生的图案。 如果您在脑海中描绘它, 您可以看到如何再次折叠盒子。 边线形成线条, 然后沿着虚线折叠它, 以便再次创建矩形棱镜 。

    The second figure is a square pyramid . Let’s think about its parts and how it might look if it was unfolded.  The base is a square and there are four triangles on the sides. You can unfold it from the vertex down. Here is what it looks like.
    ::第二个数字是平方金字塔。 让我们想想它的部件,如果它被展出,它会是什么样子。 基座是一个方形,边上有四个三角形。 您可以从顶端向下展出它。 这就是它的外观。

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    You can see that if you fold on the dotted lines, the faces are rejoined, forming a vertex at the top of the figure.
    ::你可以看到,如果你折叠在虚线上, 脸部会重新组合, 在图上方形成一个顶点 。

    The last figure is a cylinder . You know that the base and the top of a cylinder are circles. Think about the middle as a rectangle that is wound around the edges of the circles. 
    ::最后一个数字是圆柱形。 你知道圆柱形的底部和顶部是圆圈。 把中间想象成圆圈边缘的矩形。

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    Now let's look at a cone.
    ::现在让我们来看看锥体。

    When looking at a cone from the front, you see a triangle . When you look from the bottom, you see a circle .  When looking at the cone from above, you see a circle with a point in the center.  The point represents the top of the cone.  The circle represents the base.
    ::从前面看锥体时,可以看到三角形。从下面看,可以看到圆。从上面看锥体时,可以看到圆。从上面看,可以看到圆锥体,中间有一个点。圆点代表锥体的顶部。圆形代表底部。

    Imagine the triangle that you see from the front wrapping around the circular base, forming the vertex at the top.  The net of a cone looks like this:
    ::想象一下您从圆形底部前围上圆形的三角形, 在顶部形成顶部的顶端。 锥形网看起来是这样的 :

    Nets let you see the shape of the base, as well as the side or faces, of a all at once.
    ::网让您看到基地的形状, 以及侧面或面孔, 即刻看到全部的形状。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Michael and Amy's unknown boxes.
    ::早些时候,你得到一个问题 关于迈克尔和艾米的未知盒子。

    With regard to the first box:
    ::关于第一个方框:

    First, all of the faces are .
    ::首先,所有的脸都是。

    Next, there are four rectangular side faces.
    ::接下来,有四个长方形面孔。

    Then, there are two rectangular end faces.  When folded, these represent the base and top.
    ::然后,有两个矩形端面。折叠后,这些面面面代表底部和顶部。

    The answer for the first box is it is a rectangular prism.
    ::第一个盒子的答案是 它是一个矩形棱柱。

    With regard to the second box:
    ::关于第二个方框:

    First, all of the faces are squares.
    ::首先,所有的脸都是方形的。

    Next, there are four square side faces.
    ::接下来,有四张正方面孔。

    Then, there are two square end faces. When folded, these represent the base and the top.
    ::然后,有两张正方端的面孔。折叠后,这些面孔代表基座和顶层。

    The answer for the second box is it is a cube.
    ::第二个盒子的答案是它是一个立方体。

    Example 2
    ::例2

    Draw the net of a pentagonal prism .
    ::绘制五角形棱镜的网状。

    First, draw the top and base of the pentagonal prism, remembering that the top and base of any prism is the same shape.
    ::首先,绘制五角形棱镜的顶部和底部,记住任何棱镜的顶部和底部都是相同的形状。

    Next, draw the rectangular side faces of the pentagonal prism, remembering that there are five edges on the base (and top) and that this is the same as the number of faces on the side.
    ::接下来,绘制五角棱镜的矩形侧面, 记住底部( 和顶部) 有五个边缘, 这与侧面的面数相同 。

    The answer is that the net of a pentagonal prism looks like this:
    ::答案是,五角棱镜的网形看起来是这样的:

    Example 3
    ::例3

    What solid figure is represented by the following net?
    ::以下净额代表的实数是多少?

    First, observe that there is one six-sided figure - a hexagon - representing the base of the figure.
    ::首先,指出有一个六面数字 -- -- 六边形 -- -- 代表数字的基数。

    Next, observe that there are six triangles that make up the side faces of the figure.
    ::接下来,观察数字的侧面有六个三角形。

    Then, observe that the six triangles meet in the center which will form a vertex at the top when folded.
    ::然后观察六个三角形在中间相遇 折叠时,在顶部形成一个顶部的顶部

    The answer is the solid figure represented by the net above is a hexagonal pyramid.
    ::答案是上述净额代表的坚实数字是六边形金字塔。

    Example 4
    ::例4

    Draw the net of a triangular prism .
    ::绘制三角棱镜的网。

    First, draw the top and base of the triangular prism, remembering that the top and base of any prism is the same shape.
    ::首先,绘制三角棱镜的顶部和底部,记住任何棱镜的顶部和底部都是相同的形状。

           

    Next, draw the rectangular side faces of the triangular prism, remembering that there are three edges on the base (and top) and that this is the same as the number of faces on the side.
    ::接下来,绘制三角棱镜的矩形侧面,记住底部(和顶部)有三个边缘,这与侧面面数相同。

    Then, draw each of the different sections as one picture, with the base and top triangles in the appropriate positions around the side rectangles.
    ::然后将每个不同的区域画成一幅图片, 底三角形和顶三角形在侧矩形周围的适当位置上。

    The answer is that the net of a triangular prism looks like this:
    ::答案是三角棱镜的网形看起来是这样的:

    Review
    ::回顾

    Identify each solid by its net.
    ::以每块固体的净额来识别每块固体。

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    11. Draw an example of a new net for each of the figures in numbers 1–10.
      ::为数字 1 - 10 中的每个数字绘制新净额的示例 。

    Review (Answers)
    ::回顾(答复)

    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 。

    Resources
    ::资源