Section outline

  • General

    Collapse all Expand all

  • 半半径和直径圆环的区域和环环

    In This Lesson
    ::在本课程中

    You will learn how to find the area and of circles using radius and diameter . Use the interactive to help you manipulate the circles to find the equations for the area and circumference of circles. 
    ::您将学习如何使用半径和直径找到区域及圆圈。 使用交互来帮助您操控圆圈, 以找到圆圈区域和环形的方程 。

    Parts of a Circle
    ::圆圆的一部分

    A circle is a 2-dimensional figure such that all of the points are the same distance (the radius) from a fixed point (the center ). The radius is a line segment where one endpoint is the center of the circle and the other is on the circle. The diameter of a circle is a line segment with both endpoints on the circle and also passes through the center. The length of the diameter is the same as two radii (plural for radius). In mathematical terms, this would be written   The distance around a circle is called the circumference . Place the vocabulary terms in the correct spot in the picture below.  
    ::圆是一个二维图, 使所有点与固定点( 中心) 的距离( 半径) 相同。 半径是一条线段, 其中一端点是圆的中心, 另一端是圆的圆。 圆的直径是一条线段, 圆上有两个端点, 也穿过圆的中心。 直径与两个半径( 半径) 的长度相同 。 从数学角度来说, 这将会被写入 。 圆周围的距离被称为环绕 。 将词汇术语设置在下方的正确位置 。

    Discussion Question
    ::讨论问题

    What tool do you think would be best for measuring the circumference of a circle? What challenges would you have measuring the circumference with a circle?
    ::你认为哪种工具最适合测量圆环的环形?用圆衡量环形有什么挑战?

    Let's Go Bowling!
    ::我们去打保龄球吧!

    Ernesto and Tyler are heading to the bowling alley. They both want to figure out how many revolutions the bowling ball takes until it gets to the end of the lane and hits the pins. The faster they can do this, the harder the ball will hit the pins and, hopefully, the better their game will get. The typical bowling ball has a diameter of 8.5 inches and a lane is 60 feet long. How many revolutions does it take the ball to travel down the lane?
    ::Ernesto和Tyler正前往保龄球道。他们都想弄清楚保龄球要经过多少次革命才能到达车道的尽头,然后撞上钉子。他们越快做到这一点,球就会越打针,而且,希望他们的比赛越好。典型的保龄球直径为8.5英寸,车道长60英尺。有多少次革命需要球沿着车道走?

    In the interactive, the bowling ball is at the beginning of the lane. Drag the red dot on the ball to show its path down the lane. Every time the ball has one revolution, a line will appear to mark it, to help you determine the number of revolutions.
    ::在互动中, 保龄球在车道的起点 。 拖住球上的红色点显示球沿车道的路径 。 每次球发生一次革命, 就会出现一条线来标记它, 帮助您确定革命的数量 。

    In this interactive, you defined  and found the formula for circumference. It will be helpful to memorize this formula in both forms. In addition, you discovered that one revolution of a circle (or bowling ball) is the same its circumference.
    ::在此互动中, 您定义并找到了环绕的公式 。 这将会有助于以两种形式记住这个公式 。 此外, 您发现圆圈( 或保龄球) 的革命是相同的环绕 。

    Let's switch to finding the area of a circle.  How could you use the circumference of a circle to find its area?
    ::我们切换到找到圆的区域。你如何使用圆的环绕来找到它的区域?

    Orange-You Interested?
    ::橙色,你感兴趣吗?

    Your little brother loves playing with his food. Your mom wants him to learn  while playing and she decides to give you both a slice from an orange. She asks, "Can you figure out how much orange you are eating?" You, being older and wiser than your little brother, decide to measure the circumference of the slice. He  rips  the orange rind and unfolds all the segments so that they all look like little triangles in a row. How could you use what your brother did and the circumference to find the area of the circular slice of orange?
    ::你弟弟喜欢玩自己的食物。你妈妈想让他在玩耍时学习,她想用橙子给你们俩一片。她问道,“你能不能弄清楚你在吃多少橙子?”你比弟弟年长聪明,决定测量切片的宽度。他撕开橙汁,将各片展开,使其看起来像一连串的小三角形。你怎么能用你哥哥的所作所为和宽度来发现橘子圆形片的面积呢?

    In the interactive, you will start with the slice. Click on the blue  button at the top of the orange to "unfold" or rip the slice open. Then, take half of the orange segments and rotate them so that they fit into the other segments to make a sort of . Use this to determine the formula for the area of a circle.
    ::在互动中,您将从切片开始。 单击橙色顶部的蓝色按钮以“ 翻开” 或撕开切片。 然后, 将一半的橙色片段进行旋转, 使其与其他部分相容, 从而做出某种 。 使用它来决定圆形区域的公式 。

    Hint: The is the same as that of a rectangle ;  base  × height .
    ::提示: 与矩形相同; 基数 x 高度。

    Discussion Question
    ::讨论问题

    You just derived the formula for the area of a circle using orange segments!  The area of any circle is A = π r 2  Discuss what all the parts of the formula mean.
    ::您只是用橙色段来推断圆形区域的公式! 任何圆形的面积都是 Ar2 讨论公式的所有部分的含义 。

       Summary
    ::摘要

    • A circle is a set of points that are the same distance (the radius) from a fixed point (the center).
      ::一个圆是一组点,与固定点(中心)的距离(半径)相同。
    • The diameter is a line segment that passes through the center and endpoints are on the circle.
      ::直径是一条穿过中间线的线段,端点在圆上。
    •  is defined as  and is commonly approximated as 3.14.
      ::定义是,并且通常约合3.14。
    • The formula for circumference is C = 2 π r  or  C = π d  
      ::环绕公式为 C=2r 或 Cd
    • The formula for the area is A = π r 2   
      ::区域的公式为 Ar2