9.15 圆环环

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  圆环环

  

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  The theme of the school dance this year is “The 50’s.” For decorations, the 7 ^th grade class is gathering old records and gluing a sparkly trim around the edges. How much trim do they need for each record if its diameter is 12 inches?
  ::今年学校舞蹈的主题是“50年代 ” 。 对于装饰品来说,七年级班正在收集旧纪录,在边缘周围布满闪闪发光的短片。 如果每张记录直径为12英寸,他们需要多少修剪?

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  In this concept, you will learn how to find the circumference of a circle using a given diameter.
  ::在此概念中,您将学会如何用给定直径找到圆环环。

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  Finding the Circumference of a Circle
  ::寻找圆环环

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  The perimeter is the total distance around the edges of a two-dimensional shape. To find the perimeter of a shape made from line segments, such as a square or triangle , you simply add the lengths of the sides together.
  ::周界是二维形状边缘周围的总距离。 要找到由线段(如方形或三角形)形成的形状的周界, 您只需将两维形状的长度加在一起即可 。

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  $\begin{array}{r}{P}_{\text{Square}}=s+s+s+s\text{or}{P}_S=4s\end{array}$    
  ::PSquare=s+s+s+s+s或PS=4s

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  $\begin{array}{r}{P}_{\text{Triangle}}=s_1+s_2+s_3\end{array}$  
  ::PTriangle=s1+s2+s3 组合键=s1+s2+s3

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  The perimeter of a circle is called the circumference and is equal to the total distance around the edge .
  ::圆环的周界称为环绕,等于边缘周围的总距离。

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  The diameter , d, of a circle is the straight-line measurement from one point on the circle to another point on the circle that passes directly through the circle’s center .
  ::圆的直径, d,是一个圆的直径是从圆上一个点到圆上另一个点的直线测量,该点直接穿过圆的中心。

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  A circle is a unique shape in that every point along the circumference is exactly the same distance from the circle’s center. This measurement of one half the diameter is called the radius , r.
  ::圆是一个独特的形状, 环绕的每个点都与圆圈的中心完全相同。 直径的一半的测量方法叫做半径, r。

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  $\begin{array}{r}d=2r\end{array}$  
  ::d=2r d=2r

  

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  One of the unique qualities of a circle is that its diameter and circumference have a proportional relationship . This means that no matter what size the circle is, the proportional relationship , or ratio , between its circumference and diameter is always the same.
  ::圆圈的独特特性之一是其直径和环绕具有比例关系。这意味着无论圆圈大小,其周圆和直径之间的比例关系或比例总是相同的。

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  The formula for the circumference of a circle is the value of pi times the circle’s diameter:  $\begin{array}{r}C=\pi d\end{array}$
  ::圆环的公式是圆的直径比值的倍数: Cd

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  Since the diameter is twice the radius, the formula can also be written:  $\begin{array}{r}C=2\pi r\end{array}$  
  ::由于直径是半径的两倍,也可以写出公式: C=2r

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  You already know that pi is an irrational number and goes on forever. The rounded value of pi, 3.14, is usually used for calculations.
  ::您已经知道 Pi 是一个非理性的数字, 并且会一直持续下去。 pi 的四舍五入值 3. 14 通常用于计算 。

  

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  Let’s look at an example.
  ::让我们举个例子。

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  The circles above have different radii and different circumferences. Use these values and the circumference formula to solve for pi.
  ::上述圆圈有不同的弧度和环形。 使用这些值和环形公式来解决 pi 。

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  First, substitute the values of the first circle into the circumference equation.
  ::首先,将第一个圆的值替换为环形方程。

  $\begin{array}{r}6.28=\pi \times 2\end{array}$

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  Next, perform the necessary calculations to isolate $\begin{array}{r}\pi \end{array}$ .
  ::接下来,执行必要的计算 分离 。

  $$\begin{array}{r}\begin{array}{rcl}6.28÷2& =& \pi \times 2÷2\\ 3.14& =& \pi \end{array}\end{array}$$

   

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  Then, substitute the values of the second circle into the equation.
  ::然后,将第二个圆的值替换为方程。

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  $\begin{array}{r}12.56=\pi \times 4\end{array}$  
  
  Perform the necessary calculations to isolate $\begin{array}{r}\pi \end{array}$ .
  ::12.564 进行必要的计算,以分离 _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

  $$\begin{array}{r}\begin{array}{rcl}12.56÷4& =& \pi \times 4÷4\\ 3.14& =& \pi \end{array}\end{array}$$

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  Pi is what is called a constant. It always stays the same.
  ::Pi就是所谓的常数。它总是保持不变。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about the school dance decorations.
  ::之前,你在学校的舞蹈装饰上 遇到一个问题

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  The students need to know how much sparkly trim they will need to go around each record if its diameter is 12 inches.
  ::学生们需要知道,如果每个记录的直径是12英寸,他们需要多少闪烁的修剪才能翻遍每一个记录。

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  First, write down the formula.
  ::首先,写下公式。

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  $$\begin{array}{r}C=\pi d\end{array}$$

   
  ::Cd

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  Next, substitute in what you know.
  ::下一位,你所知道的替代

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  $$\begin{array}{r}C=3.14\times 12\end{array}$$

  
  ::C=3.14x12

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  Then, multiply to solve the equation.
  ::然后,乘以解答方程式。

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  $$\begin{array}{r}C=37.68\text{inches}\end{array}$$

  
  ::C=37.68英寸 C=37.68英寸

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  The answer is the circumference is 21.98 inches. The students will probably round this up to 38 inches.
  ::答案是周长为21.98英寸 学生们可能会把这里围起来38英寸

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  Example 2
  ::例2

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  Find the circumference of the circle below.
  ::查找下方圆的环形。

  

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  First write down the formula.  
  ::先写下公式

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  $\begin{array}{r}C=\pi d\end{array}$
  ::Cd

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  Next, substitute in what you know.
  ::下一位,你所知道的替代

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  $$\begin{array}{r}\begin{array}{rcl}C& =& \pi \times 8\\ C& =& 3.14\times 8\end{array}\end{array}$$

  
  ::C8C=3.14×8

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  Then, multiply to solve the equation.  
  ::然后,乘以解答方程式。

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  $\begin{array}{r}C=25.12\end{array}$
  ::C=25.12 C=25.12

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  If you were to unroll the circle into a flat line, it would be 25.12 inches long. The answer is the circumference,  $\begin{array}{r}C=25.12in\end{array}$ .  
  ::如果将圆向平面线上拉开,则长度为25.12英寸。答案是环形,C=25.12英寸。

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  Example 3
  ::例3

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  What is the circumference of the circle below?
  ::下面圆圈的环度是多少?

  

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  First, write down the formula.
  ::首先,写下公式。

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  $$\begin{array}{r}C=\pi d\end{array}$$

  
  ::Cd

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  Next, substitute in what you know.
  ::下一位,你所知道的替代

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  $$\begin{array}{r}\begin{array}{rcl}C& =& \pi \times 12.7\\ C& =& 3.14\times 12.7\end{array}\end{array}$$

  
  ::C12.7C=3.14×12.7

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  Then, multiply to solve the equation, and round.
  ::然后,乘以解答方程,然后圆。

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  $$\begin{array}{r}C=39.878\end{array}$$

  
  ::C=39.878 C=39.878

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  The answer is the circumference, $\begin{array}{r}C=39.88m\end{array}$ .
  ::答案是环形,C=39.88米

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  Example 4
  ::例4

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  Find the circumference of the circle given the radius.
  
  

  

  
  ::查找圆周的环形, 以给定圆周圆的半径 。

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  First, remember that the diameter is twice the radius, and use the formula that includes that variable.
  ::首先,记住直径是半径的两倍, 并使用包含该变量的公式 。

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  $$\begin{array}{r}C=2\pi r\end{array}$$

  
  ::C=2r

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  Next, substitute in the values that you know.
  ::接下来,取代你所知道的价值观。

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  $$\begin{array}{r}C=2(3.14)(3)\end{array}$$

  
  ::C=2(3.14)(3)

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  Then, multiply.
  ::然后,乘数。

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  $$\begin{array}{r}C=18.84\end{array}$$

  
  ::C=18.84 C=18.84

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  The answer is 18.84 inches.
  ::答案是18.84英寸

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  Example 5
  ::例5

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  Find the circumference of a circle with a diameter of 5 inches.
  ::找到一个直径为5英寸的圆圈环绕。

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  First, write down the formula.
  ::首先,写下公式。

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  $$\begin{array}{r}C=\pi d\end{array}$$

  
  ::Cd

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  Next, substitute in what you know.
  ::下一位,你所知道的替代

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  $$\begin{array}{r}C=3.14\times 5\end{array}$$

  
  ::C=3.14×5

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  Then, multiply to solve the equation.
  ::然后,乘以解答方程式。

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  $$\begin{array}{r}C=15.7\end{array}$$

  
  ::C=15.7 C=15.7

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  The answer is the circumference, $\begin{array}{r}C=15.7\text{inches}\end{array}$ .
  ::答案是环形 C=15.7英寸

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  Review
  ::回顾

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  Find the circumference of each circle given the radius or the diameter. Use 3.14 for the value $\begin{array}{r}\pi \end{array}$  and round your answer to the nearest hundredths place where needed.
  ::根据半径或直径,查找每个圆的环形。值为 ° 时使用 3.14 ,然后按需要将您的回答绕到最接近的百位位置。

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  1. radius = 2 in
     ::半半径= 2 英寸
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  2. diameter = 4 ft
     ::直径=4英尺
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  3. radius = 4.5 in
     ::半半径=4.5英寸
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  4. diameter = 8 meters
     ::直径=8米
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  5. radius = 12 inches
     ::半径 = 12 英寸
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  6. diameter = 12 mm
     ::直径=12毫米
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  7. radius = 14 mm
     ::半径=14毫米
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  8. diameter = 13 feet
     ::直径=13英尺
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  9. radius = 10 inches
     ::半径 = 10 英寸
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  10. diameter = 7.5 feet
      ::直径=7.5英尺
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  11. radius = 2.5 inches
      ::半径=2.5英寸
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  12. radius = 5.6 feet
      ::半径=5.6英尺
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  13. diameter = 3.75 feet
      ::直径=3.75英尺
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  14. diameter = 4.5 feet
      ::直径=4.5英尺
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  15. diameter = 10.75 meters
      ::直径=10.75米

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源