6.10 三角棱晶体量-interactive

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• 选择节三角棱晶体体积

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  三角棱晶体体积

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  Triangular Prisms
  ::三角棱柱

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  To help extend our knowledge of to triangular prisms, let's revisit area .
  ::为了帮助我们把对三角棱镜的了解扩大到三角棱镜, 让我们重新审视一下区域。

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. What is the area of the following triangle ? Each box is one square unit .
  ::1. 下列三角形的面积是多少?每个方框是一个平方单位。

  

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  2. If the triangle above was 3-dimensional with a height of one square unit, how many unit cubes could fit in the shape?
  ::2. 如果上方三角形为三维,高度为一平方单位,形状内可装多少个立方体?

  

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  3. How many cubes would there be in 2 of these figures?
  ::3. 其中两个数字中有多少立方体?

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  4. How many cubes would there be in n of these figures?
  ::4. 在这些数字中, n 将有多少立方体?

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  5. What formula could we use to find the number of cubes in n of these figures for a triangle with any dimensions .    
  ::5. 对于具有任何维度的三角形,我们用何种公式来找到这些数字中以 n 表示的立方体数。

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  Cookie Dough
  ::饼干口袋

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  A brand of cookie dough, Raw Enough, sells chocolate chip cookie dough in triangular-prism-shaped packages where the base is a right isosceles triangle . They come in two sizes and are measured by the quantity of cookies the batch makes.
  ::一种牌子饼干面团,Raw Nennid, 在三角体形的包件中出售巧克力薯片饼干面团, 基底是一个右等分三角形。 它们以两个大小, 用批量的饼干数量来衡量 。

  Size	Base	Height	Cost
  1 dozen	Legs are 2 in	12 in	$3.29
  2 dozen	??	??	$5.99

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  Your job is to determine the of the 2 dozen size, based on what you know about the 1 dozen size. There are two different correct answers that you need to find. Use the interactive to determine the volume of the 1 dozen size and double the volume to get the 2 dozen size. Then stretch the prism in the interactive so that its dimensions will give the volume of the second size.
  ::您的任务就是根据您对十二个大小的了解, 来决定十二个大小的大小。 您需要找到两个不同的正确答案 。 使用互动来确定十二个大小的体积, 并将体积翻倍以获得二十个大小 。 然后在交互体积中伸展棱镜, 以便让其维度给出第二大小的体积 。

   

  

  INTERACTIVE

  Cookie Dough

  

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  • Drag the upper red dot to change the side lengths of the isosceles right triangle.
    ::拖动上方红色点以改变右三角形的等离子体侧长。
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  • Drag the lower red dot to change the height of the prism.
    ::拖曳下方红色点以改变棱镜的高度。

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  Do you want to reset the PLIX?

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  For triangular prisms, you determined that the formula for the volume could be rewritten as  $\begin{array}{r}V=\frac{1}{2}lwh\end{array}$ .  This is specific to triangular-based prisms!  If you ever forget the formula, you can still use $\begin{array}{r}V=Bh,\end{array}$  and remember that the area of the base is just the area of a triangle.  Either way will give you the correct answer.
  ::对于三角棱晶, 您确定音量的公式可以重写为 V= 12lwh。 这是基于三角棱晶的公式 。 如果您忘记公式, 您仍然可以使用 V= Bh, 并记住基底区域只是三角区域。 无论哪种方式, 您都会得到正确的答案 。

   

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  Would You Like (Another) Slice  of Pizza?
  ::你想吃披萨吗?

  The pizza restaurant, Vinny's By the Slice, sells pizza by the slice.  He has special to-go boxes that hold one slice of pizza for his customers that don't want a whole pizza. The boxes themselves are equilateral triangular prisms and he has three different sizes; small, medium, and large. Now, he wants to determine the volume of the piece of pizza he can put in the boxes. 

  Pizza Size	Box Edge Length	Box Height
  Small	4 in	2 in
  Medium	6 in	2 in
  Large	8 in	2 in

  Use the interactive to determine the size of each box, and then the volume. You will need to adjust the dots on the corners in order to get the correct dimensions.

   

   

   

   

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  There are several types of triangles and any could be a base of a triangular prism . Typically, it will be an equilateral or right triangle . Remember, for a right triangle, the legs will be the base and height (in the area formula), but for any other type of triangle you need to be given the height, also called the .
  ::三角形有几种类型, 任何类型的三角形都可能是三角棱柱的基底。 通常, 它是一个等边或右三角形。 记住, 对于右三角形, 右三角形的腿将是基数和高度( 在区域公式中) , 但是对于任何其他类型的三角形, 您需要给定高度, 也称为高度 。

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     Summary
  ::摘要

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  • The formula for the volume of a prism is the area of the base times the height,  $\begin{array}{r}V=bh.\end{array}$  
    ::棱晶体积的公式是基数高度的面积,V=bh。
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  • The formula for the volume of a triangular prism can be written as $\begin{array}{r}V=\frac{1}{2}lwh,\end{array}$  where $\begin{array}{r}l\end{array}$  is the length of the base and $\begin{array}{r}w\end{array}$  is the height of the base.
    ::三角棱晶体积的公式可以以 V=12lwh 写成,其中,l 是基数的长度, w 是基数的高度。
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  • To find the area of the base, $\begin{array}{r}B,\end{array}$  or the height, $\begin{array}{r}h,\end{array}$  given the volume, divide the volume by the other given measurement.
    ::要找到基准区域, B 或高度, h , 根据体积, 将体积除以其他给定测量。