章节大纲

  • lesson content

    Karen and Lance are building a backyard playground for their two children. They have a swing  set , a merry-go-round, and a sandbox already set up. Lance is going to the store to buy sand for the sandbox and needs to know how much sand it can hold. The sandbox is 6 feet wide, 8 feet long, and 1 feet deep. How can Lance use a formula to calculate the total   of this sandbox?
    ::凯伦和兰斯正在为他们的两个孩子建造一个后院操场。他们有一个秋千、一个旋转木马和一个沙箱。兰斯将去商店买沙箱用的沙子,需要知道有多少沙子。沙箱宽6英尺、8英尺长、1英尺深。兰斯如何使用公式来计算沙箱的总数?

    In this concept, you will learn to find volumes of rectangular and triangular prisms using formulas.
    ::在此概念中,您将学会使用公式找到大量矩形和三角棱晶。

    Finding Volume of Prisms
    ::寻找棱晶体量

    Volume  is the amount of  space  inside a  .
    ::音量是 .

    Filling  with cubes is a simple, easy way to understand volume. If you can count the cubes, you can figure out the volume. However, sometimes you will have to figure out the volume of a  prism  when there aren’t any cubes drawn inside it.
    ::用立方体填充是一个简单、容易理解音量的方法。 如果您可以计算立方体, 您可以找到音量 。 然而, 有时当没有立方体时, 您必须找出棱晶的体积 。

    Take a look at the prism below.
    ::看看下面的棱镜

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    This  rectangular prism  has a  height  of 5 inches, a width of 3 inches, and a length of 4 inches.
    ::这种矩形棱镜的高度为5英寸,宽度为3英寸,长度为4英寸。

    Here is a formula for finding the volume of this type prism.
    ::这是找到这种棱柱的量的公式。

    V = B h

    B  means the  area  of the base, which is the length times the width, and  h  means the height.
    ::B 表示基数的区域,即宽度的长度倍数,h 表示高度。

    So, first figure out the area of the base.
    ::所以,首先找出基地的面积。

    A = 3 × 4 = 12

    Next, multiply  B  by  h .
    ::下一个乘以B乘以h

    h = 5 V = 12 × 5 = 60

    The volume is 60 cubic inches or  i n 3 .  Remember, volume is in  cubic units .
    ::音量为 60 立方英寸或 i n 3。 记住, 音量为立方单位 。

    Let’s look at another example. Find the volume using the volume formula.
    ::让我们看看另一个例子。 用音量公式查找音量 。

    lesson content

    V = B h

    First, figure the area of the base.
    ::首先,图图基地的面积。

    The area of the base is  2 × 8 = 16
    ::基数区域为 2 × 8 = 16

    Next, multiply the  B  by  h . The height is 3 inches.
    ::下一个乘以 B 乘以 h 。 高度为 3 英寸 。

    V = 16 × 3 V = 48   i n 3

    The volume of this rectangular prism is  48   i n 3 .
    ::此矩形棱柱的体积为 48 i n 3 。

    You can use the same formula for finding the volume of the  triangular prism . Except this time, the area of the base is a  triangle  and not a  rectangle .
    ::您可以使用相同的公式来查找三角棱晶的体积。除了这次外,基础区域是一个三角区域,而不是矩形。

    Take a look at the triangular prism below.
    ::看看下面的三角棱镜。

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    To find the volume of a triangular prism, multiply the area of the base ( B ) with the height of the prism.
    ::要找到三角棱镜的体积, 请将基点( B) 的面积乘以棱镜的高度 。

    V = B h

    First, find the area of the triangular base using the formula for area of a triangle.
    ::首先,使用三角形区域的公式查找三角基点区域。

    A = 1 2 b h A = 1 2 ( 15 × 6 ) A = 1 2 ( 90 ) A = 45  sq. units

    Next, multiply this by the height.
    ::下一个,乘以这个乘以高度。

    V = B h V = ( 45 ) h V = 45 ( 2 ) V = 90   cubic centimeters or   c m 3

    The volume of the prism is  90   c m 3 .
    ::棱晶的体积是90厘米3

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Lance and Karen’s sandbox.
    ::更早之前, 兰斯和凯伦的沙箱问题就发生在你身上。

    The sandbox is 6 feet wide, 8 feet long, and 1 feet deep. Lance needs to know the volume.
    ::沙箱宽6英尺,长8英尺,深1英尺

    To find the volume of the sandbox, which is a prism with one of its bases removed, use the following formula.
    ::要找到沙箱的体积, 沙箱是一个棱镜, 其基地之一被拆除, 使用以下公式 。

    V = B h

    First, substitute in the given values. Remember,  B  is length times width.
    ::首先, 替换给定值。 记住, B 是长度乘以宽度 。

    V = ( 8 × 6 ) ( 1 ) V = 48   f t 3

    This is the total volume.
    ::这是总量。

    Next, to find out how much sand he needs to fill the sandbox halfway, divide the total volume by 2.
    ::接下来,为了找出他需要多少沙子来填满沙箱的中途, 将总量除以2。

    48 ÷ 2 = 24

    Lance needs 24 cubic feet of sand to fill the sandbox halfway.
    ::兰斯需要24立方英尺的沙子 填满沙箱中途

    Example 2
    ::例2

    Find the volume of the prism.
    ::寻找棱镜的体积 。

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    To find the volume of a prism, use the following formula.
    ::要找到棱晶的体积,请使用以下公式。

    V = B h

    First, substitute in the given values. Remember  B  is length times width.
    ::首先, 替换给定值。 记住 B 是长度乘以宽度 。

    V = ( 16 × 9 ) ( 4 ) V = 576   c m 3

    The answer is  576   c m 3 .
    ::答案是576米3

    Example 3
    ::例3

    Find the volume of the prism.
    ::寻找棱镜的体积 。

    lesson content

    First, to find the volume of a prism, use the following formula.
    ::首先,要找到棱晶的体积,请使用以下公式。

    V = B h

    Next, substitute in the given values. Remember  B  is length times width. This is a  square  cube, so the length, width, and height are the same.
    ::接下来,在给定值中替换。 记住 B 是长度乘以宽度。 这是一个方形立方体, 长度、 宽度和高度相同 。

    V = ( 5 × 5 ) ( 5 ) V = 125   i n 3

    The answer is  125   i n 3 .
    ::答案是125 i n 3。

    Example 4
    ::例4

    Find the volume of the prism.
    ::寻找棱镜的体积 。

    lesson content

    First, to find the volume of a prism, use the following formula.
    ::首先,要找到棱晶的体积,请使用以下公式。

    V = B h

    First, substitute in the given values. Remember,  B  is length times width.
    ::首先, 替换给定值。 记住, B 是长度乘以宽度 。

    V = ( 30 × 5 ) ( 3 ) V = 450   i n 3

    The answer is  450   i n 3 .
    ::答案是450 i n 3。

    Example 5
    ::例5

    Find the volume of the prism.
    ::寻找棱镜的体积 。

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    To find the volume of a triangular prism, multiply the area of the base ( B ) with the height of the prism.
    ::要找到三角棱镜的体积, 请将基点( B) 的面积乘以棱镜的高度 。

    V = B h

    First, find the area of the triangular base using the formula for area of a triangle.
    ::首先,使用三角形区域的公式查找三角基点区域。

    A = 1 2 b h A = 1 2 ( 5 × 7 ) A = 1 2 ( 35 ) A = 17.5   s q .   m

    Next, multiply this by the height.
    ::下一个,乘以这个乘以高度。

    V = B h V = ( 17.5 ) 1 V = 17.5   c m 3

    The volume of the prism is  17.5   c m 3 .

    ::棱晶体积为17.5厘米3米。

    Review
    ::回顾

    Find the volume of each rectangular prism. Remember to label your answer in cubic units.
    ::查找每个矩形棱柱的体积。 记住要将答案标签为立方单位 。

    1. Length = 5 in, width = 3 in, height = 4 in
      ::长度 = 5 英寸,宽 = 3 英寸,身高 = 4 英寸
    2. Length = 7 m, width = 6 m, height = 5 m
      ::长度=7米,宽度=6米,高度=5米
    3. Length = 8 cm, width = 4 cm, height = 9 cm
      ::长度 = 8 厘米,宽 = 4 厘米,高度 = 9 厘米
    4. Length = 8 cm, width = 4 cm, height = 12 cm
      ::长度 = 8 厘米,宽 = 4 厘米,高度 = 12 厘米
    5. Length = 10 ft, width = 5 ft, height = 6 ft
      ::长度 = 10英尺,宽 = 5英尺,高度 = 6英尺
    6. Length = 9 m, width = 8 m, height = 11 m
      ::长度=9米,宽度=8米,高度=11米
    7. Length = 5.5 in, width = 3 in, height = 5 in
      ::长度=5.5英寸,宽度=3英寸,身高=5英寸
    8. Length = 6.6 cm, width = 5 cm, height = 7 cm
      ::长度=6.6厘米,宽度=5厘米,高度=7厘米
    9. Length = 7 ft, width = 4 ft, height = 6 ft
      ::长度 = 7 英尺,宽 = 4 英尺,高度 = 6 英尺
    10. Length = 15 m, width = 8 m, height = 10 m
      ::长度=15米,宽度=8米,高度=10米

    Find the volume of each triangular prism. Remember that  h  means the height of the triangular base and  H  means the height of the whole prism.
    ::查找每个三角棱柱的体积。 记住, h 表示三角基点的高度, H 表示整个棱柱的高度。

    1. b = 6   i n ,   h = 4   i n ,   H = 5   i n  
      ::b = 6 i n, h = 4 i n, H = 5 i n
    2. b = 7   i n ,   h = 5   i n ,   H = 9   i n  
      ::b = 7 i n, h = 5 i n, H = 9 i n
    3. b = 10   m ,   h = 8   m ,   H = 9   m  
      ::b = 10米,h = 8米,H = 9米
    4. b = 12   m ,   h = 10   m ,   H = 13   m  
      ::b = 12米,h = 10米,H = 13米
    5. b = 8   c m ,   h = 6   c m ,   H = 9   c m  
      ::b = 8厘米,h = 6厘米,H = 9厘米

    Answer true or false for each of the following questions.
    ::回答下列每个问题是否真实或虚假。

    1. Volume is the amount of space that a figure can hold inside it.
      ::体积是数字中可以容纳的空间数量。
    2. The volume of a rectangular prism is always greater than the volume of a cube.
      ::矩形棱柱的体积总是大于立方体的体积。
    3. The volume of a triangular prism is less than a rectangular prism with the same size base.
      ::三角棱镜的体积小于大小相同的矩形棱镜。
    4. A painter would need to know the surface area of a house to do his/her job correctly.
      ::画家需要知道房子的表面 才能正确地完成他/她的工作
    5. If Marcus is covering his book with a book cover, Marcus is covering the surface area of the book.
      ::如果马库斯用书封面遮盖他的书, 马库斯就覆盖书的表面面积。