节: 使用单位立方体的棱镜体积 | 10.15使用单位立方体的棱镜体积

章节大纲

Jerry’s assignment in his carpentry class is to build a wooden storage container that will hold at least 48 cubic units of material. Jerry has already started on the rectangular container, which is 4 units wide and 2 units long. Jerry isn’t sure what height the container should be in order to hold a of 48 cubic units. How can Jerry use this information to determine the height of the container?
::杰里在其木工班上的任务是建造一个至少储存48立方单位材料的木制储存容器。杰里已经开始使用长4个单位宽和2个单位长的长方形容器。杰里不确定容器应该高到什么高度才能持有48立方单位。杰里如何利用这一信息来确定容器的高度?

In this concept, you will learn to identify the volume of prisms using unit cubes.
::在这个概念中,你将学会使用单元立方体来识别棱晶体的体积。

Finding Volume of Prisms Using Unit Cubes
::使用单元立方体查找棱晶体量

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

These cubes make up a rectangular prism . The cubes represent the volume of the prism . This prism is five cubes by two cubes by one cube. In other words, it is five cubes long, by two cubes high by one cube wide. You can multiply each of these values together to get the volume of the rectangular prism.
::这些立方体组成了一个矩形棱柱。立方体代表了棱柱的体积。这个棱柱是五个立方体乘两个立方体乘一个立方体。换句话说, 这是五个立方体长, 两个立方体乘两个立方体高一个立方体宽。您可以将这些数值乘在一起, 以获得矩形棱柱的体积。

$\begin{aligned} 5 \times 2 \times 1 = 10 cubic units \end{aligned}$
::5×2×1=10立方单位

The volume of the rectangular prism is 10 cubic units or units ³ . The units are cubic units because you multiplied the units 3 times when you multiplied the height, length, and width.
::矩形棱晶体体积为 10 立方单位或单位3。这些单位是立方单位3。因为乘以高度、长度和宽度,单位乘以3倍。

Here is another prism.
::这是另一个棱镜。

First, to figure out the volume of this prism, identify the measurements.
::首先,要找出这个棱镜的体积, 确定测量数据。

Length - 6
::长度 - 6

Width - 6
::宽度 - 6

Height - 6
::高度-6

Next, substitute these values in the formula for volume then solve.
::其次,用公式中这些值替换音量,然后解决。

$\begin{aligned} \begin{array}{rcl} Length \times Width \times Height & = & Volume in cubic units \\ 6 \times 6 \times 6 & = & 216 cubic units \end{array} \end{aligned}$

The volume of the cube is 216 cubic units.
::立方体的体积是216立方体单位。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jerry and the storage container he is building.
::早些时候,有人给了你一个问题关于杰瑞和他正在建造的储藏箱。

The container is 4 units wide and 2 units long when he learned about the volume requirement. The container needs to have a volume of 48 cubic units. How can Jerry use this information to determine the height the container should be?
::容器宽4个单位,宽2个单位,当他了解容量要求时,容器需要48立方单位的体积。

First, to figure the height the container should be, identify the given measurements.
::首先,为了确定容器应处于的高度,应标明给定的测量量。

Length - 2 units
::长度 - 2个单元

Width - 4 units
::宽度 - 4 个单位

Height - ?
::- 身高 - 身高?

Volume - 48 cubic units
::音量 - 48立方单位

Next, substitute these values into the formula for volume.
::其次,将这些值替换为量的公式。

$\begin{aligned} \begin{array}{rcl} Length \times Width \times Height & = & Volume in cubic units \\ 2 \times 4 \times H & = & 48 cubic units \end{array} \end{aligned}$

Then, multiply.
::然后,乘数。

$\begin{aligned} 8 (H) = 48 \end{aligned}$

Then, divide both sides by 8.
::然后,将双方除以8。

$\begin{aligned} H = 6 units \end{aligned}$

The container should have a height of 6 units.
::集装箱的高度应为6个单位。

Example 2
::例2

What is the volume of this figure?
::这个数字的量是多少?

First, to figure out the volume of this prism, identify the measurements.
::首先,要找出这个棱镜的体积, 确定测量数据。

Length - 4 units
::长度 - 4个单元

Width - 4 units
::宽度 - 4 个单位

Height - 3 units
::高度 - 3个单位

Next, substitute these values into the formula for volume then solve.
::其次,将这些值替换为音量公式,然后解析。

$\begin{aligned} \begin{array}{rcl} Length \times Width \times Height & = & Volume in cubic units \\ 4 \times 4 \times 3 & = & 216 cubic units \end{array} \end{aligned}$

The volume of the prism is 48 cubic units, or 48 units ³ .
::棱晶体积为48立方单位,或48立方单位3。

Example 3
::例3

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

First, to figure out the volume of this prism, identify the measurements.
::首先,要找出这个棱镜的体积, 确定测量数据。

Length - 1
::长度 - 1

Width - 2
::宽度-2

Height - 5
::高度 - 5

Next, substitute these values into the formula for volume then solve.
::其次,将这些值替换为音量公式,然后解析。

$\begin{aligned} \begin{array}{rcl} Length \times Width \times Height & = & Volume in cubic units \\ 1 \times 2 \times 5 & = & 10 cubic units \end{array} \end{aligned}$

The volume of the prism is 10 cubic units.
::棱晶体积是10立方单位。

Example 4
::例4

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

First, to figure out the volume of this prism, identify the measurements.
::首先,要找出这个棱镜的体积, 确定测量数据。

Length - 2 inches
::长度 - 2英寸

Width - 4 inches
::宽度 - 4英寸

Height - 2 inches
::高度 - 2 英寸

Next, substitute these values into the formula for volume then solve.
::其次,将这些值替换为音量公式,然后解析。

$\begin{aligned} \begin{array}{rcl} Length \times Width \times Height & = & Volume in cubic units \\ 2 \times 4 \times 2 & = & 16 cubic inches \end{array} \end{aligned}$

The volume of the cube is 16 cubic inches.
::立方体的体积是16立方英寸

Example 5
::例5

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

First, to figure out the volume of this prism, identify the measurements.
::首先,要找出这个棱镜的体积, 确定测量数据。

Length - 2 inches
::长度 - 2英寸

Width - 4 inches
::宽度 - 4英寸

Height - 1 inch
::高度 - 1英寸

Next, substitute these values into the formula for volume then solve.
::其次,将这些值替换为音量公式,然后解析。

$\begin{aligned} \begin{array}{rcl} Length \times Width \times Height & = & Volume in cubic units \\ 2 \times 4 \times 1 & = & 8 cubic units \end{array} \end{aligned}$

The volume of the prism is 8 cubic inches.

::棱晶的体积是8立方英寸

Review
::回顾

Find the volume of each prism.
::查找每个棱镜的体积。

::[表8]

::[图9]

::[图10]

::[表11]

::[图12]

::[图13]

::[表14]

::[图15]

::[图16]

::[图17]

Identify each type of prism.
::确定每类棱晶。

::[图18]

::[图19]

::[图20]

::[图21]

章节大纲

Finding Volume of Prisms Using Unit Cubes ::使用单元立方体查找棱晶体量

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Finding Volume of Prisms Using Unit Cubes
::使用单元立方体查找棱晶体量

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾