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  • 复合三维固体表面面积

    In This Lesson
    ::在本课程中

    Y ou will be given solids that are made up of two or more prisms, pyramids , or both. To find the of these types of solids, you will need to break them apart  into smaller prisms you are familiar with. Use your knowledge of surface area to find the areas of the faces you are interested in, so you can find the surface area of the composite solid . 
    ::您将得到由两种或两种以上棱晶、金字塔或两者组成的固体。 要找到这些类型的固体, 您需要把它们分割成你熟悉的较小棱晶。 使用您对表面积的了解来找到您感兴趣的面部区域, 这样您就可以找到复合固体的表面区域 。

    Pool Construction
    ::池池建设

    Your parents are putting in a swimming pool!  The dimensions are in the image below, and also in the interactive .
    ::你父母在放游泳池! 维度在下面的图像中, 互动中也是如此。

    Swimming pool dimensions including length, width, and depth measurements for construction calculations.
    Swimming Pool Dimensions

    After the hole is dug, the contractor needs to line the entire pool with shotcrete, a type of concrete that can be sprayed into place with a large hose. To line the pool will cost $8.50 a square foot. How much shotcrete will your parents need for the pool and how much will it cost? Use the interactive below. To find out how much shotcrete is needed, you will need to determine the total surface area of the walls and bottom of the pool. If you need a hint, click "Show Hint". 
    ::挖洞后, 承包人需要用胶片胶片标定整个池塘, 这种混凝土可以用大水管喷洒。 要排成水池, 每平方英尺需要8.50美元。 父母需要多少针片胶片才能挖出池子, 要花多少钱? 使用下面的交互作用。 要确定需要多少针片胶片, 您就需要确定池壁和池底的总面积。 如果您需要提示, 请点击“ Show Hint ” 。

    INTERACTIVE
    Constructing a Swimming Pool
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    • Click the buttons to observe the dimensions of the pool.
      ::单击按钮以观察游泳池的维度。
    • Drag the screen to change your point of view of the pool. Use two fingers on your trackpad or touch screen or scroll the mouse wheel to zoom.
      ::拖曳屏幕以改变您对游泳池的视图点。 在您的跟踪板上使用两根手指, 或者触摸屏幕, 或者将鼠标方向盘滚动到缩放 。
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    Discussion Question
    ::讨论问题

    How did the way you broke apart the composite shape affected your ability to find the surface area? Would different arrangements have been easier or harder? Would they all result in the same area ?
    ::你打破复合形状的方式是如何影响你找到表层面积的能力的?不同的安排是否比较容易或困难?它们是否都在同一区域?

    YourConstruct Video Game 
    ::您的构建视频游戏

    A very popular video game called YourConstruct, allows you to build worlds using different types of blocks that are in the shapes of prisms and pyramids. You decide to build a castle out of cubes, triangular prisms and pyramids. Use the interactive to build the castle, using the parameters listed below :
    ::一种非常受欢迎的电子游戏,叫做“你的构造”, 允许你使用各种形状的棱晶和金字塔构建世界。 您决定用立方体、 三角棱晶和金字塔建造一座城堡。 使用互动来建造城堡, 使用以下参数 :

    • The main building is 20 units by 24 units and 8 units tall.
      ::主楼有20个单位,24个单位,8个单位高。
    • Attached to the main building, on one of the 24 unit sides, there is another small building that is half the length of that side and 6 units in width. 
      ::在主楼24个单元侧的一侧,有另一栋小楼,其长度为该侧的一半,宽度为6个单元。
    • At each corner of the main building there are triangular spires that are 8 units tall. Each as an equilateral triangular base with edge length of 1 unit.
      ::主楼每个角落都有三角圆柱形,高8个单位,每个三角圆柱形作为边际三角基座,边缘长度为1个单位。

    Each spire is also topped with a triangular based pyramid with a height of 1 unit and an equilateral triangular base with side length of 1 unit. The building has a total of 20 windows, each one is 1 square unit in size. 10 of the windows are 3 units above the ground and the other 10 are 6 units above the ground.  
    ::每个圆柱形都有一个三角形金字塔,高度为1个单位,一个边长为1个单位的对等三角基,大楼共有20个窗口,每个窗口大小为1平方。 10个窗口位于地面上,10个窗口位于地面上,另外10个窗口位于地面上,6个窗口位于地面上。

    Each of the units in the game represents 2 feet in the real world.
    ::游戏中每个单元 代表真实世界的两英尺

    INTERACTIVE
    Castle Contstruction
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    Build an additional wing to your castle that is 8 units tall, 12 units long and 6 units in width.
    ::在你的城堡上再建一栋楼 高8个单位 长12个单位 宽6个单位

    • Move the red, blue and green points to change the values of the new wing.
      ::移动红色、蓝色和绿色点以改变新翼的值。
    • Click the button to see if your castle's wing is the correct dimensions.
      ::点击按钮来查看 您城堡的翅膀是否正确尺寸 。
    • Afterwards, construct the 4 towers around the castle so they are 8 units tall.
      ::之后,在城堡周围建造四座塔 所以它们有8个单位高
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    Determine the external surface area of your castle and how many blocks you need to build it. Find  the dimensions of the castle in the real world, remember 1 unit = 2 feet.
    ::确定您城堡的外部表面面积, 以及您要建造城堡需要多少块街区。 在现实世界中找到城堡的维度, 记住一个单位 = 2英尺 。

    Building Castles
    ::建筑城堡

    Independently or in groups, design you own castle! Then, find the surface areas of the walls and determine how many blocks you would need. Try to design the grounds and create fencing or a moat to protect the castle.
    ::独立地或集体地设计城堡,然后找到墙的表面区域,确定需要多少街区。试着设计地面,并设置栅栏或护城河,以保护城堡。

      Summary
    ::摘要

    • To find the surface area of a composite shape, divide it into smaller shapes, find the appropriate surface areas of each shape and add them together.
      ::为了找到复合形状的表面区域,将其分成较小的形状,找到每个形状的适当表面区域,并将其相加在一起。
    • Some faces may overlap, so make sure you know which faces to include or not. 
      ::有些面孔可能重叠,以确保您知道包括或不包括哪些面孔。