Course: 10.8 环境环境 | The Way To Learn

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环境

Circumference
::环境

Circumference is the distance around a circle . The circumference can also be called the perimeter of a circle. However, we use the term circumference for circles because they are round.
::环形是圆圈的距离。环形也可以称为圆圈的周界。但是, 我们使用环形的环形, 因为它们是圆形的。

Circumference Formula: $\begin{aligned} C = π d \end{aligned}$ where the diameter $\begin{aligned} d = 2 r \end{aligned}$ , or twice the radius . So $\begin{aligned} C = 2 π r \end{aligned}$ as well.
::环形公式:Cd,直径为 d=2r,或半径的两倍。C=2r。

$\begin{aligned} π \end{aligned}$ , or “pi” is the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159265358979323846...
::,或“pi”是圆环与其直径之比,大约等于314159265358979323846...

You should have a $\begin{aligned} π \end{aligned}$ button on your calculator. If you don't, you can use 3.14 as an approximation for $\begin{aligned} π \end{aligned}$ . You can also leave your answers in terms of $\begin{aligned} π \end{aligned}$ for many problems.
::您的计算器上应该有一个“ ” 按钮。否则, 您可以使用 3. 14 作为“ ” 的近似值。您也可以用“ ” 来回答许多问题。

What if you were given the radius or diameter of a circle? How could you find the distance around that circle?
::如果给您一个圆的半径或直径, 您如何找到圆周围的距离 ?

Examples
::实例

Example 1
::例1

Find the circumference of a circle with a radius of 7 cm.
::查找圆周圆的半径为 7 厘米。

Plug the radius into the formula.
::将半径插进公式中。

\begin{aligned} C = 2 π (7) = 14 π \approx 44 c m \end{aligned}

::C=2(7)=1444厘米

Example 2
::例2

The circumference of a circle is $\begin{aligned} 64 π \end{aligned}$ units. Find the diameter.
::圆环的环形为64 ° 单位。查找直径。

Again, you can plug in what you know into the circumference formula and solve for $\begin{aligned} d \end{aligned}$ .
::再一次,你可以插入你所知道的在环形公式中,并解决 d。

\begin{aligned} 64 π & = π d \\ 64 u n i t s & = d \end{aligned}

::64d64单位=d

Example 3
::例3

A circle is inscribed in a square with 10 in. sides. What is the circumference of the circle? Leave your answer in terms of $\begin{aligned} π \end{aligned}$ .
::一个圆被刻在一个方形中,有 10 平方。圆的环绕是什么? 请用 \ 的词回答。

From the picture, we can see that the diameter of the circle is equal to the length of a side. $\begin{aligned} C = 10 π i n \end{aligned}$ .
::从图片中,我们可以看到圆的直径等于一面的长度。 C=10英寸英寸。

Example 4
::例4

Find the perimeter of the square in Example 3. Is it more or less than the circumference of the circle? Why?
::在例3中找到方形的周界。它是否或多或少于圆圈的环形? 为什么?

The perimeter is $\begin{aligned} P = 4 (10) = 40 i n \end{aligned}$ . In order to compare the perimeter with the circumference we should change the circumference into a decimal.
::周界是P=4(10)=40英寸。为了比较周界和周界,我们应该将周界改为小数点。

$\begin{aligned} C = 10 π \approx 31.42 i n \end{aligned}$ . This is less than the perimeter of the square, which makes sense because the circle is inside the square.
::C=1031.42英寸,这小于方形的周界,这有道理,因为圆盘在方形内。

Example 5
::例5

The tires on a compact car are 18 inches in diameter. How far does the car travel after the tires turn once? How far does the car travel after 2500 rotations of the tires?
::一辆紧凑车的轮胎直径为18英寸。轮胎翻转一次后车程有多远?轮胎转动2500次后车程多远?

One turn of the tire is the circumference. This would be $\begin{aligned} C = 18 π \approx 56.55 i n \end{aligned}$ . 2500 rotations would be $\begin{aligned} 2500 \cdot 56.55 i n a p p r o x 141, 375 i n \end{aligned}$ , 11,781 ft, or 2.23 miles.
::轮胎的转角是环形,在2500年2500轮转时C=1856.55,大约250056.55,大约141 375英寸,11,781英尺,或2.23英里。

Review
::回顾

Fill in the following table. Leave all answers in terms of $\begin{aligned} π \end{aligned}$ .
::填写下表,将所有答案保留在_________________________

	*diameter*	*radius*	*circumference*
1.	15
2.		4
3.	6
4.			$\begin{aligned} 84 π \end{aligned}$
5.		9
6.			$\begin{aligned} 25 π \end{aligned}$
7.			$\begin{aligned} 2 π \end{aligned}$
8.	36

Find the circumference of a circle with $\begin{aligned} d = \frac{20}{π} c m \end{aligned}$ .
::查找 d=20 cm 圆圆的环形。

Square $\begin{aligned} P Q S R \end{aligned}$ is inscribed in $\begin{aligned} ⨀ T \end{aligned}$ . $\begin{aligned} R S = 8 \sqrt{2} \end{aligned}$ .
::PQSR广场的注册号为QT.RS=82。

Find the length of the diameter of $\begin{aligned} ⨀ T \end{aligned}$ .
::查找 & T 的直径长度。

How does the diameter relate to $\begin{aligned} P Q S R \end{aligned}$ ?
::直径与PQSR有何关系?

Find the perimeter of $\begin{aligned} P Q S R \end{aligned}$ .
::找到PQSR的周边

Find the circumference of $\begin{aligned} ⨀ T \end{aligned}$ .
::找到"T"的环绕

For questions 14-17, a truck has tires with a 26 in diameter.
::对于问题14-17,一辆卡车的轮胎直径为26英寸。

How far does the truck travel every time a tire turns exactly once? What is this the same as? Round your answer to the nearest tenth.
::每次轮胎完全翻转一次,卡车要走多远?

How many full rotations will the tire turn after the truck travels 1 mile? (1 mile = 5280 feet)
::卡车行驶1英里之后,轮胎将转转多少轮椅? (1英里=5280英尺)

The truck has travelled 4072 tire rotations. How many miles is this? Round your answer to the nearest hundredths place.
::卡车已经经过4072个轮胎轮转,这是多少英里?

The average recommendation for the life of a tire is 30,000 miles. How many full rotations is this?
::轮胎的平均寿命建议是30,000英里,这是多少次完全旋转?

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。

Section outline

General

环境

Circumference ::环境

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)