9.18 圆宽区域半径或直径

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  圆形给定区域半径或直径

  

   

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  Clara took her little sister, Grace, to the fish pond at the local park. Grace saw a penny in the center of the pond and wanted Clara to reach it for her. A sign stated that the area of the pond was 113.04 sq. ft. Can Clara reach the penny without falling in?
  ::Grace在池塘中央看到一分钱,希望Clara能帮她找到。 有迹象表明池塘的面积是113.04平方英尺,克拉拉能否不跌入池塘?

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  In this concept, you will learn how to find the radius (and diameter) of a circle if you know its area.
  ::在这个概念中,如果您知道圆的面积,您将学会如何找到圆的半径(和直径)。

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  Finding the Radius or Diameter of a Circle Given Area
  ::查找圆形给定区域的半径或直径

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  The formula for the area of a circle, $\begin{array}{r}A=\pi r^2\end{array}$ , can also be used to solve for the radius and diameter .
  ::圆的面积公式Ar2也可以用来解析半径和直径。

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  Let’s look an example.
  ::让我们举个例子。

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  The area of a circle is 113.04 square inches. What is its radius?
  ::圆的面积是113.04平方英寸。圆的半径是多少?

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=\pi r^2\end{array}$$

  
  ::阿 r2

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

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  $$\begin{array}{r}113.04=(3.14)r^2\end{array}$$

  
  ::113.04=(3.14)r2

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  Next, begin isolating the $\begin{array}{r}r\end{array}$  by dividing both sides of the equation by 3.14.
  ::接下来,开始隔离方程式 将方程式的两边除以3.14

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  $$\begin{array}{r}36=r^2\end{array}$$

  
  ::36=r2

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  Then, take the square root of both sides.
  ::然后,从双方的平方根开始

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  $$\begin{array}{r}6=r\end{array}$$

  
  ::6=r 6=r

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  The answer is $\begin{array}{r}r=6\end{array}$ . The radius of the circle is 6 inches.
  ::答案是 r=6. 圆的半径为 6 英寸。

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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  Clara and Grace, who were at the circular 113.04 sq. ft. fish pond.
  ::早些时候,你曾听说克拉拉和格蕾丝有问题, 他们出现在113.04平方英尺的鱼池周刊上。

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  Clara wondered if she could reach a penny in the middle without falling in.
  ::克拉拉想知道她能否在中途达到一分钱 而不掉进去

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=\pi r^2\end{array}$$

  
  ::阿 r2

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

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  $$\begin{array}{r}113.04=(3.14)r^2\end{array}$$

  
  ::113.04=(3.14)r2

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  Then, begin isolating the $\begin{array}{r}r\end{array}$  by dividing both sides of the equation by 3.14.
  ::然后,开始孤立 r 通过将方程的两边除以3.14。

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  $$\begin{array}{r}36=r^2\end{array}$$

  
  ::36=r2

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  Take the square root of both sides.
  ::以双方的平方根。

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  $$\begin{array}{r}6=r\end{array}$$

  
  ::6=r 6=r

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  The answer is $\begin{array}{r}r=6\end{array}$ . The radius of the circle is 6 feet. Unless Clara wants to swim with the goldfish, she’d best leave the penny where it is!
  ::答案是 r=6. 圆的半径是 6 英尺。 除非克拉拉想和金鱼一起游泳, 否则她最好把硬币放在哪里!

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  Example 2
  ::例2

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  What is the diameter of a circle if its area is $\begin{array}{r}379.94c{m}^2\end{array}$ ?
  ::如果圆的面积是379.94厘米,圆的直径是什么?

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=\pi r^2\end{array}$$

  
  ::阿 r2

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

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  $$\begin{array}{r}379.94=(3.14)r^2\end{array}$$

  
  ::379.94=(3.14)r2

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  Next, begin isolating the $\begin{array}{r}r\end{array}$  by dividing both sides of the equation by 3.14.
  ::接下来,开始隔离方程式 将方程式的两边除以3.14

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  $$\begin{array}{r}121=r^2\end{array}$$

  
  ::121=r2

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  Then, take the square root of both sides.
  ::然后,从双方的平方根开始

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  $$\begin{array}{r}11=r\end{array}$$

  
  ::11=r 11=r

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  Remember that you are solving for the diameter.
  ::记住,你正在解决直径问题。

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  $$\begin{array}{r}\begin{array}{rcl}d& =& 2r\\ d& =& 2\times 11\\ d& =& 22\end{array}\end{array}$$

  
  ::d=2rd=2x11d=22

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  The answer is the diameter, $\begin{array}{r}d=22cm\end{array}$ .
  ::答案是直径, d=22厘米。

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  Example 3
  ::例3

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  Solve for the radius of a circle if  $\begin{array}{r}\text{area}=153.86sq.in.\end{array}$
  ::如果区域=153.86 sq. in,则解决圆的半径。

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=\pi r^2\end{array}$$

  
  ::阿 r2

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

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  $$\begin{array}{r}153.86=(3.14)r^2\end{array}$$

  
  ::153.86=(3.14)r2

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  Next, begin isolating the $\begin{array}{r}r\end{array}$  by dividing both sides of the equation by 3.14.
  ::接下来,开始隔离方程式 将方程式的两边除以3.14

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  $$\begin{array}{r}49=r^2\end{array}$$

  
  ::49=r2

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  Then, take the square root of both sides.
  ::然后,从双方的平方根开始

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  $$\begin{array}{r}7=r\end{array}$$

  
  ::7=r

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  The answer is $\begin{array}{r}r=7\end{array}$ . The radius of the circle is 7 inches.
  ::答案是 r=7. 圆的半径为 7 英寸。

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  Example 4
  ::例4

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  Find the radius of a circle with an area of 379.94 sq. ft.
  ::查找圆的半径,其面积为379.94平方米。

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=\pi r^2\end{array}$$

  
  ::阿 r2

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

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  $$\begin{array}{r}379.94=(3.14)r^2\end{array}$$

  
  ::379.94=(3.14)r2

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  Then, begin isolating the $\begin{array}{r}r\end{array}$  by dividing both sides of the equation by 3.14.
  ::然后,开始孤立 r 通过将方程的两边除以3.14。

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  $$\begin{array}{r}121=r^2\end{array}$$

  
  ::121=r2

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  Take the square root of both sides.
  ::以双方的平方根。

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  $$\begin{array}{r}11=r\end{array}$$

  
  ::11=r 11=r

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  The answer is $\begin{array}{r}r=11\end{array}$ . The radius of the circle is 11 feet.
  ::答案是 r=11,圆的半径是11英尺

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  Example 5
  ::例5

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  The area of a circle is 452.16 sq. m. Find its radius.
  ::圆的面积是452.16平方米。 找出其半径。

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=\pi r^2\end{array}$$

  
  ::阿 r2

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

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  $$\begin{array}{r}452.16=(3.14)r^2\end{array}$$

  
  ::452.16=(3.14)r2

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  Then, begin isolating the $\begin{array}{r}r\end{array}$  by dividing both sides of the equation by 3.14.
  ::然后,开始孤立 r 通过将方程的两边除以3.14。

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  $$\begin{array}{r}144=r^2\end{array}$$

  
  ::144=r2

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  Take the square root of both sides.
  ::以双方的平方根。

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  $$\begin{array}{r}12=r\end{array}$$

  
  ::12=r 12=r

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  The answer is $\begin{array}{r}r=12\end{array}$ . The radius of the circle is 12 meters.
  ::答案是 r=12,圆的半径是12米

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  Review
  ::回顾

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  Use 3.14 for the value $\begin{array}{r}\pi \end{array}$  and round your answer to the nearest tenths place where needed.
  ::以 3. 14 表示 ° 的值,并按需要将您的回答折到最近的十分位。

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  Find each radius given the area of the circle.
  ::查找给定圆的面积的每个半径 。

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  1. 12.56 sq. in.
     ::12.56平方米英寸
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  2. 78.5 sq. m
     ::78.5平方米米
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  3. 200.96 sq. cm
     ::200.96平方米cm
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  4. 254.34 sq. in.
     ::254.34平方米英寸
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  5. 7.07 sq. ft.
     ::7.07平方米(吨)
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  6. 28.26 sq. m
     ::28.26平方米米

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  Find each diameter given the area of the circle.
  ::查找给定圆形区域的每个直径 。

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  7. 12.56 sq. in.
     ::12.56平方米英寸
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  8. 78.5 sq. m
     ::78.5平方米米
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  9. 200.96 sq. cm
     ::200.96平方米cm
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  10. 254.34 sq. in.
      ::254.34平方米英寸
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  11. 7.07 sq. ft.
      ::7.07平方米(吨)
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  12. 28.26 sq. m
      ::28.26平方米米
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  13. 615.44 sq. ft.
      ::615.44平方米
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  14. 176.625 sq. m
      ::176.625平方米
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  15. 113.04 sq. ft.
      ::113.04平方米

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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