9.16 圆环环的直径或半径

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 圆环的直径或半径

  Collapse Expand

  圆环的直径或半径

  

  播放段落

  Rebekah’s family went to a circular corn maze and spent a couple hours trying to find their way out. The distance around the outside of the maze was posted as 1 mile, or 5,280 feet. Rebekah wondered how far she would walk if she were able to cut right through the middle.
  ::Rebekah的家人去了环形玉米迷宫,花了几个小时寻找出路。 迷宫外的距离被贴在1英里或5,280英尺的距离上。 Rebekah想知道如果她能从中间切开,她会走多远。

  播放段落

  In this concept, you will learn to find the diameter and radius of a circle if you are given the .
  ::在此概念中, 如果给您给定 , 您将学会找到圆的直径和半径 。

  播放段落

  Finding the Diameter and Radius of a Circle Given Circumference
  ::寻找圆环环的直径和半径

  播放段落

  The formula for the circumference of a circle, $\begin{array}{r}c=\pi d\end{array}$  or $\begin{array}{r}c=2\pi r\end{array}$ , can also be used to find the diameter or radius of a circle.
  ::cd或c=2r圆环绕的公式也可以用来查找圆的直径或半径。

  播放段落

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

  播放段落

  A circle has a circumference of 20.72 m. What is its diameter?
  ::圆的环度为20.72米。 圆的直径是多少?

  播放段落

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

  播放段落

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

  
  ::d

  播放段落

  Next, fill in the values that you know.
  ::接下来,填充您知道的值 。

  播放段落

  $$\begin{array}{r}20.72m=3.14d\end{array}$$

  
  ::20.72米=3.14 d

  播放段落

  Then, divide both sides of the equation by 3.14
  ::然后,将等式两边除以3.14。

  播放段落

  $$\begin{array}{r}6.6=d\end{array}$$

  
  ::6.6=d

  播放段落

  The answer is the diameter is 6.6 meters.
  ::答案是直径是6.6米

  播放段落

  You can check your answer by substituting your answer in the original equation.
  ::您可以在原始方程中替换您的答案来检查您的答案 。

  播放段落

  $$\begin{array}{r}\begin{array}{rcl}c& =& \pi d\\ 20.72& =& (3.14)(6)\\ 20.72& =& 20.72\end{array}\end{array}$$

  The answer checks.
  ::cd20.72=(3.14)(6)20.72=20.72 回答查询。

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about Rebekah at the corn maze with a 5,280 ft circumference.
  ::早些时候,有人给了你一个问题 关于Rebekah 在玉米迷宫 5,280英尺宽。

  播放段落

  She wondered how far she would have to walk if she were able to cut right across.
  ::她想知道,如果她能够直截了当地穿过去,她必须走多远才能走多远。

  播放段落

  First, recognize that you are solving for the diameter, the straight- line distance through the middle of the circle from one point on the circumference to another.
  ::首先, 承认您正在解决直径, 直径直线距离, 从环绕的一个点到另一个点, 穿过圆的中间。

  播放段落

  Then, write the formula.
  ::那么,写公式。

  播放段落

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

  
  ::d

  播放段落

  Next, fill in the values that you know.
  ::接下来,填充您知道的值 。

  播放段落

  $$\begin{array}{r}5,280=(3.14)d\end{array}$$

  
  ::5,280=(3.14)d

  播放段落

  Then, perform the calculations necessary to isolate $\begin{array}{r}d\end{array}$ .
  ::然后进行分离所需的计算。

  播放段落

  $$\begin{array}{r}\begin{array}{rcl}1,681.528662& =& d\\ 1,681.5\text{feet}& =& d.\end{array}\end{array}$$

  
  ::1,681.5英尺=1,681.5英尺。

  播放段落

  The answer is the $\begin{array}{r}\text{diameter}=1,681.5\end{array}$  feet. Rebekah would have to walk 1,681.5 feet if she were able to walk the diameter of the corn maze.
  ::答案是直径=1,681.5英尺。Rebekah如果能够走玉米迷宫直径,则必须走1,681.5英尺。

  播放段落

  Example 2
  ::例2

  播放段落

  The circumference of a circle is 147.58 yards. Find its radius.
  ::圆环的环形是147.58码 找到它的半径

  播放段落

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

  播放段落

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

  
  ::c=2r

  播放段落

  Next, fill in the values that you know.
  ::接下来,填充您知道的值 。

  播放段落

  $$\begin{array}{r}147.58=2(3.14)r\end{array}$$

  
  ::147.58=2(3.14)r

  播放段落

  Then, perform the calculations necessary to isolate $\begin{array}{r}r\end{array}$ .
  ::然后,进行必要的计算 分离r。

  播放段落

  $$\begin{array}{r}\begin{array}{rcl}147.58& =& 6.28r\\ 147.58& =& 6.28r\\ 23.5& =& r\end{array}\end{array}$$

  The answer is $\begin{array}{r}r=23.5\end{array}$  yards.
  ::147.58=6.28 r147.58=6.28 r23.5=r 答案是r=23.5码。

  播放段落

  Example 3
  ::例3

  播放段落

  The circumference is 28.26 inches. What is the diameter?
  ::环形28.26英寸,直径是多少?

  播放段落

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

  播放段落

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

  
  ::d

  播放段落

  Next, fill in the values that you know.
  ::接下来,填充您知道的值 。

  播放段落

  $$\begin{array}{r}28.26=3.14d\end{array}$$

  
  ::28.26=3.14d 28.26=3.14d

  播放段落

  Then, divide both sides of the equation by 3.14
  ::然后,将等式两边除以3.14。

  播放段落

  $$\begin{array}{r}9=d\end{array}$$

  
  ::9=d 9=d

  播放段落

  The answer is the diameter is 9 inches.
  ::答案是直径是9英寸

  播放段落

  Example 4
  ::例4

  播放段落

  The circumference is 21.98 feet. What is the radius?
  ::环形是21.98英尺 半径是多少?

  播放段落

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

  播放段落

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

  
  ::c=2r

  播放段落

  Next, fill in the values that you know.
  ::接下来,填充您知道的值 。

  播放段落

  $$\begin{array}{r}21.98=2(3.14)r\end{array}$$

  
  ::21.98=2(3.14r)

  播放段落

  Then, perform the calculations necessary to isolate $\begin{array}{r}r\end{array}$ .
  ::然后,进行必要的计算 分离r。

  播放段落

  $$\begin{array}{r}\begin{array}{rcl}21.98& =& 6.28r\\ 3.5& =& r\end{array}\end{array}$$

  
  ::21.98=6.28 r3.5=r

  播放段落

  The answer is $\begin{array}{r}r=3.5\end{array}$  feet.
  ::答案是r=3.5英尺。

  播放段落

  Review
  ::回顾

  播放段落

  Use 3.14 for the value $\begin{array}{r}\pi \end{array}$  and round your answer to the nearest hundredths place where needed.
  ::以 3. 14 表示 值,然后按需要将您的回答绕到最接近的百分百位 。

  播放段落

  Given the circumference, find the diameter.
  ::根据周长 找到直径

  播放段落
  1. Circumference = 15.7 ft.
     ::环形=15.7英尺
  播放段落
  2. Circumference = 20.41 in
     ::环环境=20.41英寸
  播放段落
  3. Circumference = 21.98 m
     ::环形=21.98米
  播放段落
  4. Circumference = 4.71 cm
     ::环形=4.71厘米
  播放段落
  5. Circumference = 47.1 ft
     ::环形=47.1英尺

  播放段落

  Given the circumference, find the radius.
  ::根据周长 找到半径

  播放段落
  6. Circumference = 43.96 in
     ::环环境=43.96英寸
  播放段落
  7. Circumference = 15.7 m
     ::环形=15.7米
  播放段落
  8. Circumference = 14.13 in
     ::环环境=14.13英寸
  播放段落
  9. Circumference = 20.41 cm
     ::环形=20.41厘米
  播放段落
  10. Circumference = 12.56 ft.
      ::环状=12.56英尺

  播放段落

  Solve each problem.
  ::解决每一个问题。

  播放段落
  11. What is the circumference of a circle whose diameter is 32.5 meters?
      ::直径为32.5米的圆圈的环形是什么?
  播放段落
  12. A circle has a radius of 67 centimeters. What is its circumference?
      ::圆的半径为67厘米。圆的周长是多少?
  播放段落
  13. What is the circumference of a circle whose radius is 7.23 feet?
      ::半径为7.23英尺的圆圈的环形是什么?
  播放段落
  14. What is the diameter of a circle whose circumference is 172.7 inches?
      ::环形为172.7英寸的圆圈的直径是多少?
  播放段落
  15. A circle has a circumference of 628 centimeters. What is the radius of the circle?
      ::一个圆的周长为628厘米。圆的半径是多少?
  播放段落
  16. The circumference of a circular table is 40.82 feet. What is the radius of the rug?
      ::圆形表的周长为40.82英尺。地毯的半径是多少?
  播放段落
  17. Workers at the zoo are building five circular pens for the elephants. Each pen has a diameter of 226 meters. How much fence will the workers need in order to surround all five pens?
      ::动物园的工人正在为大象建造五支圆形笔。 每支笔的直径为226米。 工人需要多少围栏才能包围所有五支笔?
  播放段落
  18. Mrs. Golding has a circular mirror with a frame around it. The frame is 4 inches wide. If the diameter of the mirror and the frame together is 48 inches, what is the circumference of just the mirror?
      ::Golding夫人有一个圆形镜子,上面有圆形框架。框架宽4英寸。如果镜子和框架的直径加在一起是48英寸,那么只有镜子的环形是什么?

  播放段落

  Review (Answers)
  ::回顾(答复)

  播放段落

  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 。

  播放段落

  Resources
  ::资源