课程： 9.7 棱晶体量-interactive

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棱晶体量
Cubic Units
::立三次单位

In this lesson, you are going to be looking at 3- d imensional objects. While 2-dimensional objects are measured in square units , 3-dimensional are measured using cubic units .
::在此课中, 您将查看三维天体。虽然二维天体用平方单位测量, 但用立方单位测量三维天体。

In the interactive below to create a 3-dimensional object with unit cubes. As you are building, think about how you could find the of three dimensional objects with unit cubes like these.
::在下面的互动中,用单元立方体创建一个三维天体。当您正在构建时,请想想如何用单元立方体找到三个维天体。

Discussion Questions
::讨论问题讨论问题

How are the properties of your object similar to that of a 2-dimensional object?
::您的天体的属性与二维天体的属性相似吗 ?

How are the properties of your object different from that of a 2-dimensional object?
::您对象的属性与二维对象的属性有何不同?

How many cubes did it take to build your structure?
::建造你的结构需要多少立方体?

Volume
::量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量

The amount of space an object takes up is known as its volume , which is measured in cubic units. The number of cubic units that you used to create an object in the opening activity was the volume of the object.
::物体接收的空间物体数量称为其体积,以立方单位计量。用于在开始活动中创建物体的立方单位数是物体的体积。

In the interactive below, explore strategies for finding the volume of a rectangular prism by rearranging unit cubes.
::在下文互动部分,探讨通过重新安排单元立方体来寻找矩形棱晶体体积的战略。

A cubic unit is a cube which is 1 unit wide, 1 unit long, and 1 unit high. This can be for any unit of measurement: a millimeter, an inch, a meter, a mile, etc. For the following interactive, you will explore what can be measured using different unit cubes and how big they are in volume relative to certain objects.
::立方体是一个立方体,宽1个单位,长1个单位,高1个单位。它可以用于任何计量单位:一毫米、一英寸、一英寸、一米、一英里等。对于以下互动,您将探索使用不同单位立方体测量什么,以及它们相对于某些对象的体积大小。

Discussion Questions
::讨论问题讨论问题

Could a cubic foot be a tool you use to find the area of a room? How would you use it to find the volume of a room?
::立方英尺是否是您用来找到房间的工具? 您如何使用它来找到房间的体积 ?

If you did not have a cubic unit what other tools could you use to find the volume of a room?
::如果您没有立方单元, 您可以用其他什么工具来找到房间的体积 ?

Volume of Rectangular Prisms
::矩形棱晶体体积

A prism is a with two congruent ends connected by quadrilaterals. The word before prism describes the shape of the base. A rectangular prism consists of two congruent connected by quadrilaterals. If the base meets all sides at a right angle , it is called a right rectangular prism.
::棱晶是一个有两端相容的晶体, 由四边形连接。棱晶之前的单词描述了基体的形状。矩形棱晶体由四边形连接的两个相似点组成。如果基点在正确的角度与所有面相匹配, 它被称为右方矩形棱柱。

Discussion Questions
::讨论问题讨论问题

What would a star prism look like?
::恒星棱镜会长什么样?

What other shapes could be used to make prisms?
::还有什么其他形状可以用来制造棱镜?

The volume of a prism can be found by counting the cubic units on the base and multiplying by the number of rows. In a rectangular prism, you can determine the area of the base by multiplying the length by the width. You can then multiply this by the height which is the number of rows. This can be represented using the following formula:
::光晶体积可以通过计数基数的立方单位和乘以行数来找到。在矩形棱柱中,您可以通过将长度乘以宽度来确定基数的面积。然后您可以乘以行数的高度。这可以用以下公式表示:

$\begin{aligned} Volume of a Rectangular Prism = length \cdot width \cdot height \end{aligned}$
$\begin{align*}\text{Volume of a Rectangular Prism} = \text{length} \cdot \text{width} \cdot \text{height}\end{align*}$
::矩形棱晶体体积=长宽度

Using the interactive below, you will practice finding the using the formula for volume given length, width, and height.
::使用下面的交互效果,您将练习找到使用体积公式的公式,公式的长度、宽度和高度为给定长度、宽度和高度。

Volume of Rectangular Prisms Continued
::矩形棱晶体量

Example
::示例示例示例示例

You have been hired by a school to build a sandbox. You must determine how many bags of sand will be needed to fill the sandbox and how much it will cost. One bag of sand will fill 0.5 cubic feet and costs $4.50.
::你被学校雇来建造沙箱。你必须确定填满沙箱需要多少袋沙子,需要多少钱。一袋沙子将填满0.5立方英尺,花费4.50美元。

For this interactive, you will design the polygon base and height of the sandbox. Then you will use these values to find the volume of sand the sandbox can hold.

::对于此互动, 您将设计多边形基点和沙箱的高度。然后您将使用这些值来找到沙箱可以支撑的沙子体积。

Example
::示例示例示例示例

A fish tank needs to hold 4,830 cubic inches of water. If the length of the fish tank is 23 inches long and the width of the fish tank is 14 inches wide, what will the height need to be to hold 4,830 cubic inches of water?
::如果鱼缸的长度是23英寸,而鱼缸的宽度是14英寸,那么要保持4 830立方英寸的水,高度是多少?

Use the formula $\begin{align*}\text{Volume} = \text{length} \cdot \text{width} \cdot \text{height}\end{align*}$ where the volume is 4830, length is 23, and width is 14. Substituting the numbers into the formula, you get:
::在音量为4830, 长度为23, 宽度为14 的公式中, 使用量值= 长度= widthQh8, 值为 4830, 值为 23, 宽度为 14 的公式中, 将数字替换为公式, 您可以得到 :

$\begin{aligned} 4830 = 23 \cdot 14 \cdot h \end{aligned}$
$\begin{align*}4830=23\cdot14\cdot h\end{align*}$
::4830=23_14_h

Then solve for the missing value, $\begin{align*}h:\end{align*}$
::然后解决缺失值, h:

$\begin{aligned} 4830 & = 23 \cdot 14 \cdot h \\ 4830 & = 322 h \\ 322 & 322 \\ 15 & = h \end{aligned}$
$\begin{align*}4830&=23\cdot14\cdot h\\ 4830&=322h\\ \hline \color{red} 322 ~ & ~~~~~ \color{red} 322 \\ 15&=h\end{align*}$ Answer: The height is 15 inches.
::4830=2314h4830=322h322 322 3215=hAnswer:高度为15英寸。

Summary
::摘要

Volume is the amount of space a 3-dimensional object takes up, measured in cubic units.
::体积是指以立方单位测量的三维天体接收的空格量。

A prism is a solid with two congruent bases that are parallel to each other and connected by quadrilaterals.
::棱镜是坚实的,具有两个相平行、四边形相连的一致基础。

The volume of a prism is the area of the base times the height. For a rectangular prism, the volume can be found using the formula $\begin{align*}V=l\cdot w\cdot h.\end{align*}$
::棱晶体积是基数高度的面积。对于矩形棱柱,用公式 V=lwh 即可找到该体积。

章节大纲

常规

棱晶体量

Cubic Units ::立三次单位

Volume of Rectangular Prisms ::矩形棱晶体体积

Volume of Rectangular Prisms Continued ::矩形棱晶体量

Summary ::摘要

Cubic Units
::立三次单位

Volume of Rectangular Prisms
::矩形棱晶体体积

Volume of Rectangular Prisms Continued
::矩形棱晶体量

Summary
::摘要