课程： 10.7给定圆周的圆的直径或半径 | The Way To Learn

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选择节给定圆周的圆的直径或半径

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给定圆周的圆的直径或半径
Marcus is helping his coach design an obstacle course for the weekend’s fitness tournament. They dug a circular water pit with a of 18 feet. Marcus has to cut a balance beam that the students will use to cross the pit. The beam is going across the center of the pit. How can Marcus determine how long the balance beam should be to cover the diameter of the pit?
::马库斯正在帮助他的教练设计周末健身比赛的障碍课程。他们挖了一个18英尺高的圆形水坑。马库斯必须切断学生跨坑时使用的平衡梁。梁横穿坑中心。马库斯如何确定平衡梁应覆盖坑直径多久?

In this concept, you will learn to find the diameter or radius of a circle given the circumference.
::在这个概念中,根据环形,您将学会找到圆的直径或半径。

Finding the Diameter or Radius
::查找直径或半径

The circumference of a circle is equal to pi times the diameter.
::圆的环绕等于直径的皮乘。

$\begin{aligned} C = π d \end{aligned}$

The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius.
::直径是半径的2倍,因此圆环的方程使用半径是半径的2倍。

$\begin{aligned} C = 2 π r \end{aligned}$

If you are given the circumference but not the radius or the diameter, you can still solve for one or the other using these formulas.
::如果给您给定环绕,但不给半径或直径,您仍然可以用这些公式解答其中之一或另一个。

Let’s look at an example.
::让我们举个例子。

INTERACTIVE

Pi

Find the diameter of a circle with a circumference of 21.98 feet.
::找到圆的直径环形为21.98英尺

To work on this problem, you will need the formula for finding the circumference of a circle using the diameter.
::要解决这个问题,你需要找到公式,用直径来寻找圆环。

$\begin{aligned} C = π d \end{aligned}$

First, fill in the given information.
::首先,填写给定信息。

$\begin{aligned} 21.98 = (3.14) d \end{aligned}$

Next, solve the problem by dividing both sides by 3.14. The 3.14 will cancel out on the right side of the equation, leaving $\begin{aligned} d \end{aligned}$ . Then divide 21.98 by 3.14.
::接下来,通过将双方除以3.14来解决问题。3.14将取消方程式右侧,离开 d。然后将21.98除以3.14。

$\begin{aligned} 3.14 \bar{) 21.98} \end{aligned}$

When dividing decimals, move the decimal point two places to make the divisor a whole number then divide as usual.
::将小数点除以小数点后,将小数点 2 移动到小数点两位,使小数点成为整数,然后按原样除以。

$\begin{aligned} 7 \\ 314 \bar{) 2198} \end{aligned}$

The answer is, the diameter is 7 feet.
::答案是直径是7英尺

You can use the same approach to solving for the radius as you did the diameter. Just remember to divide the diameter by two to get the radius.
::您可以使用与直径相同的方法来解析半径。记住要将直径除以 2 以获得半径。

If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter.
::如果要求您找到半径而不是直径,您只需将7英尺除以2,因为半径是直径的半径的一半。

$\begin{aligned} 7 \div 2 = 3.5 \end{aligned}$

The radius of the circle is 3.5 feet.
::圆的半径是3.5英尺

You can also use the circumference and radius equation.
::您也可以使用环形和半径方程式。

Practice Long Division
::长长业务司

You may use this tool to practice long division if you need a refresh on the process:
::如果您需要更新进程, 您可以使用此工具练习长分割 :

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Marcus and the obstacle course.
::之前,你遇到马库斯和障碍赛的问题

The circumference of the circular water pit is 18 feet. How can Marcus use this information to determine how long the beam needs to be to go across the center of the pit? Marcus needs to figure out the diameter of the pit.
::圆形水坑的环形范围是 18 英尺。 Marcus 如何使用这个信息来决定横穿坑中心需要多长时间? Marcus 需要找出坑的直径。

He will need to use the formula for finding the circumference of a circle using the diameter.
::他将需要使用公式来利用直径来寻找圆环的环形。

$\begin{aligned} C = π d \end{aligned}$

First, fill in the given information.
::首先,填写给定信息。

$\begin{aligned} 18 = (3.14) d \end{aligned}$

Next, solve the problem by dividing both sides by 3.14. The 3.14 will cancel out on the right side of the equation, leaving $\begin{aligned} d \end{aligned}$ . Then divide 18 by 3.14.
::接下来,通过将双方除以3.14来解决问题。3.14将取消方程式右侧,留下 d。然后将18除以3.14。

$\begin{aligned} 3.14 \bar{) 18.00} \end{aligned}$

When dividing decimals, move the decimal point two places to make the divisor a whole number then divide as usual.
::将小数点除以小数点后,将小数点 2 移动到小数点两位,使小数点成为整数,然后按原样除以。

$\begin{aligned} 5.72 \\ 314 \bar{) 1800.00} \end{aligned}$

The diameter is 5.72 feet, so the beam needs to be at least that long.
::直径是5.72英尺所以光束至少需要那么长

Example 2
::例2

Use the equation for the circumference of a circle to answer the following question.
::使用圆环的方程来回答下面的问题。

What is the radius of a circle with a circumference of 34.54 feet?
::环绕34.54英尺的圆圆的半径是多少?

To work on this problem, you will need the formula for finding the circumference of a circle using the diameter.
::要解决这个问题,你需要找到公式,用直径来寻找圆环。

$\begin{aligned} C = π d \end{aligned}$

First, fill in the given information.
::首先,填写给定信息。

$\begin{aligned} 34.54 = (3.14) d \end{aligned}$

Next, solve the problem by dividing both sides by 3.14. The 3.14 will cancel out on the right side of the equation, leaving $\begin{aligned} d \end{aligned}$ . Then divide 34.54 by 3.14.
::接下来,通过将双方除以3.14来解决问题。3.14将取消方程式右侧,离开 d。然后将34.54除以3.14。

$\begin{aligned} \overset{}{3.14 \bar{) 34.54}} \end{aligned}$

When dividing decimals, move the decimal point two places to make the divisor a whole number then divide as usual.
::将小数点除以小数点后,将小数点 2 移动到小数点两位,使小数点成为整数,然后按原样除以。

$\begin{aligned} 11 \\ 314 \bar{) 3454} \end{aligned}$
The diameter of this circle is 11 feet.

Then, because the radius is half of the diameter, divide the diameter by 2.
::然后,因为半径是直径的一半,直径除以2。

$\begin{aligned} \frac{11}{2} = 5.5 \end{aligned}$

The radius of this circle is 5.5 feet.
::这个圆的半径是5.5英尺

Example 3
::例3

Find the diameter given the circumference.
::查找环形的直径。

$\begin{aligned} C = 31.4 m \end{aligned}$

To work on this problem, you will need the formula for finding the circumference of a circle using the diameter.
::要解决这个问题,你需要找到公式,用直径来寻找圆环。

$\begin{aligned} C = π d \end{aligned}$

First, fill in the given information.
::首先,填写给定信息。

$\begin{aligned} 31.4 = (3.14) d \end{aligned}$

Next, solve the problem by dividing both sides by 3.14.
::其次,通过将双方除以3.14来解决问题。

$\begin{aligned} 10 \\ 314 \bar{) 3140} \end{aligned}$

The diameter of this circle is 10 m.
::这个圆的直径是10米。

Example 4
::例4

Find the diameter given the circumference.
::查找环形的直径。

$\begin{aligned} C = 28.26 i n \end{aligned}$

To work on this problem, you will need the formula for finding the circumference of a circle using the diameter.
::要解决这个问题,你需要找到公式,用直径来寻找圆环。

$\begin{aligned} C = π d \end{aligned}$

First, fill in the given information.
::首先,填写给定信息。

$\begin{aligned} 28.26 = (3.14) d \end{aligned}$

Next, solve the problem by dividing both sides by 3.14.
::其次,通过将双方除以3.14来解决问题。

$\begin{aligned} 9 \\ 314 \bar{) 2826} \end{aligned}$

The diameter of this circle is 9 inches.
::这个圆的直径是9英寸

Example 5
::例5

Find the diameter given the circumference.
::查找环形的直径。

$\begin{aligned} C = 23.55 i n \end{aligned}$

To work on this problem, you will need the formula for finding the circumference of a circle using the diameter.
::要解决这个问题,你需要找到公式,用直径来寻找圆环。

$\begin{aligned} C = π d \end{aligned}$
First, fill in the given information.

$\begin{aligned} 23.55 = (3.14) d \end{aligned}$

Next, solve the problem by dividing both sides by 3.14.
::其次,通过将双方除以3.14来解决问题。

$\begin{aligned} 11 \\ 314 \bar{) 3454} \end{aligned}$

The diameter is 11 inches.

::直径11英寸

Review
::回顾

Find the diameter of each circle given the circumference. Use the value approximated value 3.14 for the number $\begin{aligned} π . \end{aligned}$
::查找每个圆形的直径, 以其环绕为条件。使用大约值 3. 14 的数值表示。

$\begin{aligned} C = 37.68 i n . \end{aligned}$
::C=37.68 i n 。

$\begin{aligned} C = 40.82 i n . \end{aligned}$
::C=40.82 i n 。

$\begin{aligned} C = 18.84 i n . \end{aligned}$
::C=18.84 i n 。

$\begin{aligned} C = 28.26 f t . \end{aligned}$
::C = 28.26 f t. = 28.26 f t.

$\begin{aligned} C = 56.52 m . \end{aligned}$
::C=56.52米。

$\begin{aligned} C = 17.27 m . \end{aligned}$
::C=17.27米。

$\begin{aligned} C = 19.468 f t . \end{aligned}$
::C=19.468 f t.

$\begin{aligned} C = 30.772 f t . \end{aligned}$
::C = 30.772 f t.

Find the radius of each circle given the circumference. Use the value approximated value 3.14 for the number $\begin{aligned} π . \end{aligned}$
::查找每个圆的半径, 并给其环绕。使用数值大约为 3. 14 的值, 编号为 + 。

$\begin{aligned} C = 25.1828 i n . \end{aligned}$
::C=25.1828 i n 。

$\begin{aligned} C = 37.68 i n . \end{aligned}$
::C=37.68 i n 。

$\begin{aligned} C = 12.56 i n . \end{aligned}$
::C=12.56 i n 。

$\begin{aligned} C = 15.7 f t . \end{aligned}$
::C=15.7英尺长。

$\begin{aligned} C = 7.85 m . \end{aligned}$
::C=7.85米。

$\begin{aligned} C = 50.24 m . \end{aligned}$
::C=50.24米。

$\begin{aligned} C = 21.98 m . \end{aligned}$
::C=21.98米。

$\begin{aligned} C = 14.13 f t . \end{aligned}$
::C = 14.13 f t.

Review (Answers)
::回顾(答复)

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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::资源

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