6.9 立方体和矩形棱晶体量-interactive
章节大纲
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In This Lesson
::在本课程中Y ou will learn about the of cubes and rectangular prisms. The volume of a 3D shape is the amount of space inside of it. The units will always be "cubic" because we are adding one more dimension. So, cubic inches, cubic feet, etc. It can also be written inches cubed or in 3 . Just like area is squared, volume is cubed.
::您将了解立方体和矩形棱柱。 立体形状的体积是其中的空格。 单位总是“ 立方体 ” , 因为我们增加了一个维度。 因此, 立方英寸、 立方英尺等等。 它也可以写成英寸立方或英寸。 与面积正方形相同, 体积是立方体 。To find the volume of a cube or rectangular prism , the process is the same. You will need to determine how much of something will fill it up.
::要找到立方体或矩形棱晶体的体积, 过程是一样的。 您需要确定有多少东西会填满它 。
Deriving the Formula
::调出公式A prism is 5 inches wide by 7 inches long and 8 inches tall. To determine the volume of the prism, fill it with unit cubes that are 1 x 1 x 1. The number of cubes will be the same as the volume. Answer the questions within the interactive and click the buttons to determine the volume of the entire prism.
::棱晶宽5英寸,长7英寸,高8英寸。要确定棱晶的体积,请用1x1x1x1的单位立方体填充。立方体的数目将与体积相同。回答互动中的问题,单击按钮确定整个棱晶的体积。From this interactive, you learned that the formula for volume is V = l w h (volume equals length times width times height) and can also be written V = B h (volume equals the area of the base times the height). Notice that the version, V = l w h is only true for rectangular prisms and cubes. However, V = B h will work for any type of prism, as long as you can find the area of the base.
::您从此互动中了解到, 音量的公式是 V=lwh( 体积等于宽度乘以高度) , 也可以写为 V=Bh( 体积等于基数乘以高度的面积 ) 。 请注意, 版本, V=lwh( V=lwh) 只适用于矩形棱柱和立方体。 然而, V=Bh( 体积等于宽度乘以高度) 将为任何类型的棱柱工作, 只要您能找到基数区域 。
Sandbox Dimensions
::沙箱尺寸Yasmani is building a sand box for his little brother. He wants the box to be 8 inches deep and he wants the width and length will be the same. Yasmani has 15 cubic feet of sand for the box. With these parameters, what is the smallest the sand box could be?
::Yasmani正在为他弟弟建造一个沙箱。他想让沙箱深8英寸,希望宽度和长度相同。Yasmani有15立方英尺的沙子。有了这些参数,沙箱中最小的是什么?-
Use the prism in the interactive and stretch the length and width so that the volume is 15 cubic feet.
::使用互动的棱镜,伸展长度和宽度,使体积达到15立方英尺。 -
The length and width are the same and the
height
is fixed at 8 inches.
::长度和宽度相同,高度固定在8英寸。 -
Move the red
point
to change the length of the red edges.
::移动红色点以更改红色边缘的长度。 -
Move the green point to change the height of the prism.
::移动绿点以改变棱晶的高度 。 -
Pay attention to the units!
::注意各单位!
Discussion Question
::讨论问题Why is it important to have all of the units be the same within an equation? for more examples!
::为什么所有单位在等式中必须相同?Make sure you understand the units used in a problem before tackling it. If you need to convert volume, remember to cube the 1-dimensional ratio! For example, since there are 12 inches in a foot, there are 12 3 cubic inches in one cubic foot. In a cubic yard there will be 3 3 feet, since there are 3 feet in a yard. The "cubic" part tells you what power to raise the unit to in order to determine the correct conversion .
::在解决问题之前, 请确定您了解在解决一个问题时所使用的单位 。 如果您需要转换音量, 请记住 立方 1 维比 。 例如, 由于一英尺有 12 英寸, 一立方英尺有 123 立方英寸 。 在一个立方的院子里, 将会有 33 英尺 , 因为一个院子里有 3 英尺 。 “ 立方” 部分告诉您, 要将这个单位提升到哪个位置以确定正确的转换 。
Cubes & Candy
::立方体和糖果Michael is making candy and wants the package to be a box that is 3 inches. If each piece of candy is a half-inch cube, how many pieces of candy can fit into the box ?
::如果每块糖果都是半英寸的立方体,有多少块糖果可以放进盒子里?-
Use the interactive to place the candy into the box.
::用互动键把糖果放进盒子里 -
Determine the volume of the box and how many candies can be put in one package.
::确定框的体积,以及可以将多少糖果放入一个包中。
Summary
::摘要-
The volume of a prism
is the area of the
base times the height,
V
=
B
h
.
::棱晶体的体积是以V=Bh为基数的高度乘以基数的面积。 -
The volume of a rectangular prism is the length times width times height,
V
=
l
w
h
.
::矩形棱柱的体积是宽度的长度乘以高度, V=lwh。 -
The volume of a cube is the length of one side cubed,
V
=
s
3
.
::立方体的体积是一面立方体的长度, V=s3。
-
Use the prism in the interactive and stretch the length and width so that the volume is 15 cubic feet.