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  • 计算衍生数量

    A scientist in a lab coat using a calculator and taking notes during calculations.

    This scientist is using a calculator. S cientific work often requires calculations. Converting units—say from inches to centimeters—is one type of calculation that might be required. Calculations may also be needed to find derived quantities.
    ::这名科学家正在使用计算器,科学工作往往需要计算。把单位从英寸转换为厘米——这是可能需要的计算方法之一。为了找到衍生的数量,也需要计算方法。

    What Are Derived Quantities?
    ::什么是衍生数量?

    Derived quantities are quantities that are calculated from two or more measurements. Derived quantities cannot be measured directly. They can only be computed. Many derived quantities are calculated in physical science . Three examples are area, volume , and density.
    ::衍生数量是指从两次或多次测量中计算的数量,不能直接测量衍生数量,只能计算。许多衍生数量是在物理科学中计算的。三个例子是面积、体积和密度。

    Calculating Area
    ::计算区域

    The area of a surface is how much space it covers. It’s easy to calculate the area of a surface if it has a regular shape, such as the blue rectangle in the sketch below. You simply substitute measurements of the surface into the correct formula. To find the area of a rectangular surface, use this formula:
    ::表面的面积是它覆盖的面积。如果表面有正常形状,例如下面的草图中的蓝色矩形,那么它很容易计算出表面的面积。您只需用正确的公式来替代对表面的测量。要找到矩形表面的面积,请使用这个公式:

    Area (rectangular surface) = length × width (l × w)

    A blue rectangle labeled with dimensions used to calculate area.

    Q: What is the area of the blue rectangle?
    ::问:蓝色矩形的面积是多少?

    A: Substitute the values for the rectangle’s length and width into the formula for area:
    ::A: 将矩形长度和宽度的值替换为区域公式:

    Area = 9 cm × 5 cm = 45 cm 2

    Q: Can you use this formula to find the area of a square surface?
    ::问题:您能否使用此公式来找到平方表面的区域?

    A: Yes, you can. A square has four sides that are all the same length, so you would substitute the same value for both length and width in the formula for the area of a rectangle.
    ::A:是的,你可以。一个方形有四面,四面长度相同,所以您可以在矩形区域公式的长度和宽度中以相同的值替换。

    Calculating Volume
    ::计算音量

    The volume of a object is how much space it takes up. It’s easy to calculate the volume of a solid if it has a simple, regular shape, such as the rectangular solid pictured in the sketch below. To find the volume of a rectangular solid, use this formula:
    ::物体的体积是它所占用的空间。如果一个固体有一个简单、正常的形状,例如以下草图中刻画的矩形固体形状,那么很容易计算其体积。要找到一个矩形固体的体积,请使用这个公式:

    Volume (rectangular solid) = length × width × height (l × w × h)

    A blue rectangular solid demonstrating dimensions for calculating volume.

    Q: What is the volume of the blue rectangular solid?
    ::问题:蓝色矩形固体的体积是多少?

    A: Substitute the values for the rectangular solid’s length, width, and height into the formula for volume:
    ::A: 将矩形固体的长度、宽度和高度值替换成体积公式:

    Volume = 10 cm × 3 cm × 5 cm = 150 cm 3

    Calculating Density
    ::计算密度

    Density is a quantity that expresses how much matter is packed into a given space. The amount of matter is its mass, and the space it takes up is its volume. To calculate the density of an object, then, you would use this formula:
    ::密度是一个表示将多少物质装入给定空间的数量。 物质的数量是质量, 空间是体积。 因此, 要计算一个对象的密度, 您将使用此公式 :

    Density = mass volume

    Q: The volume of the blue rectangular solid above is 150 cm 3 . If it has a mass of 300 g, what is its density?
    ::Q:以上蓝色矩形固体的体积为150厘米,如果质量为300克,密度是多少?

    A: The density of the rectangular solid is:
    ::A:矩形固体的密度为:

    Density = 300   g 150   cm 3 = 2   g/cm 3

    Q: Suppose you have two boxes that are the same size but one box is full of feathers and the other box is full of books. Which box has greater density?
    ::问题:假设你有两个大小相同的盒子,但一个盒子是满满的羽毛,另一个盒子是满满的书本。哪个盒子的密度更大?

    A: Both boxes have the same volume because they are the same size. However, the books have greater mass than the feathers. Therefore, the box of books has greater density.
    ::A:两个框的体积相同,因为它们大小相同。然而,书的质量大于羽毛。因此,书的密度更大。

    Units of Derived Quantities
    ::衍生数量单位

    A given derived quantity, such as area, is always expressed in the same type of units. For example, area is always expressed in squared units, such as cm 2 or m 2 . If you calculate area and your answer isn’t in squared units, then you have made an error.
    ::给定数量, 如区域, 总是以相同类型单位表示。 例如, 区域总是以平方单位表示, 如 cm2 或 m2 。 如果您计算了区域, 而答案不是平方单位, 那么您犯了错误 。

    Q: What units are used to express volume?
    ::问题:用哪些单位表示体积?

    A: Volume is expressed in cubed units, such as cm 3 or m 3 .
    ::A:音量以立方单位表示,如cm3或m3。

    Q: A certain derived quantity is expressed in the units kg/m 3 . Which derived quantity is it?
    ::问题:一定数量以单位公斤/立方米表示,取自数量是哪一数量?

    A: The derived quantity is density, which is mass (kg) divided by volume (m 3 ).
    ::A: 得出的数量是密度,即质量(公斤)除以体积(立方米)。

    Summary
    ::摘要

    • Derived quantities are quantities that are calculated from two or more measurements. They include area, volume, and density.
      ::衍生数量是指从两次或多次测量中计算的数量,包括面积、体积和密度。
    • The area of a rectangular surface is calculated as its length multiplied by its width.
      ::矩形表面的区域以其长度乘以其宽度计算。
    • The volume of a rectangular solid is calculated as the product of its length, width, and height.
      ::矩形固体的体积按其长度、宽度和高度计算。
    • The density of an object is calculated as its mass divided by its volume.
      ::物体的密度按质量除以体积计算。
    • A given derived quantity is always expressed in the same type of units. For example, area is always expressed in squared units, such as cm 2 .
      ::给定数量总是以相同类型单位表示。例如,面积总是以平方单位表示,如cm2。

    Review
    ::回顾

    1. What is a derived quantity? Give an example.
      ::数量是多少?举个例子。
    2. What are the dimensions of a square that has an area of 4 cm 2 ?
      ::面积为4厘米2的方形的尺寸是多少?
    3. Explain how you would calculate the volume of a cube.
      ::解释您如何计算立方体的体积 。
    4. Which derived quantity is used to calculate density?
      ::计算密度时使用哪一衍生数量?
    5. Which derived quantity might be measured in mm 3 ?
      ::以毫米3测量的取量是多少?

    Resources
    ::资源