Course: 9.17 圆圈面积 | The Way To Learn

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圆圆区域
Angelica’s dad is buying a round swimming pool for the yard. The brochure says $\begin{aligned} diameter = 24 f t \end{aligned}$ . What square footage of the yard will the pool cover?
::Angelica的爸爸正在为院子购买一个圆桌游泳池。小册子上写着直径=24英尺。池子覆盖的院子面积是多少?

In this concept, you will learn how to find the area of a circle .
::在这个概念中,你会学会如何找到圆圈的区域。

Finding the Area of a Circle
::查找圆圆区域

A circle is a set of connected points equidistant from a center point . The diameter is the distance across the center of the circle and the radius is the distance from the center of the circle to the edge .
::一个圆是一组连接点, 与中点等距。直径是圆中心之间的距离, 半径是圆中心与边缘之间的距离。

The number pi , $\begin{aligned} π \end{aligned}$ , is the ratio of the diameter to the . We use 3.14 to represent pi in operations. You can find the area of a circle by taking the measurement of the radius, squaring it and multiplying it by pi. Here is the formula: $\begin{aligned} A = π r^{2} \end{aligned}$ .
::数字 pi, , 是直径与直径之比。我们在操作中使用 3. 14 来代表 pi 。您可以通过测量半径、方形和乘以 pi 来找到圆形的区域。这是公式: Ar2 。

Let’s look at an example.
::让我们举个例子。

What is the area of the circle below?
::下面圆的面积是多少?

First, write the formula.
::首先,写公式。

$\begin{aligned} A = π r^{2} \end{aligned}$

::阿 r2

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

$\begin{aligned} A = (3.14) (12)^{2} \end{aligned}$

::A=( 3.14)(12) 2

Then, following the order of operations, figure out the exponent first and then multiply.
::然后,按照操作的顺序,首先找出出价,然后乘以。

$\begin{aligned} \begin{array}{rcl} A & = & (3.14) (144) \\ A & = & 452.16 s q c m \end{array} \end{aligned}$

::A=(3.14)(144) A=452.16 平方厘米

The answer is $\begin{aligned} A = 452.16 s q . c m \end{aligned}$ .
::答案是A=452.16 sq.cm。

Sometimes, you will be given a problem with the diameter and not the radius. When this happens, you can divide the measurement of the diameter by two and then use the formula.
::有时,您会遇到直径而不是半径的问题。当这种情况发生时,您可以将直径的测量除以2,然后使用公式。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Angelica and the 24-foot diameter pool.
::早些时候,你遇到安杰莉卡的问题和24英尺直径的游泳池的问题

She wants to know how many square feet of ground it would cover.
::她想知道它会覆盖多少平方英尺的土地

First, recognize that you have been given a diameter and divide by 2 to get the radius.
::首先, 承认您被赋予直径, 并用 2 来获得半径。

$\begin{aligned} \begin{array}{rcl} r & = & \frac{d}{2} \\ r & = & \frac{24}{2} \\ r & = & 12 feet \end{array} \end{aligned}$

::= rd2r=242r=12英尺

Next, substitute this value, along with pi, into the formula for the area of a circle.
::接下来,将此值与 pi 一起替换为圆区域公式。

$\begin{aligned} A = π r^{2} \end{aligned}$

::阿 r2

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

$\begin{aligned} A = (3.14) (12)^{2} \end{aligned}$

::A=( 3.14)(12) 2

Then, following the order of operations, figure out the exponent first and then multiply.
::然后,按照操作的顺序,首先找出出价,然后乘以。

$\begin{aligned} \begin{array}{rcl} A & = & (3.14) (144) \\ A & = & 452.16 s q . f t . \end{array} \end{aligned}$

::A=(3.14)(144) A=452.16 sq.ft。

The answer is $\begin{aligned} A = 452.16 s q . f t \end{aligned}$ . The round swimming pool will cover $\begin{aligned} 452.16 s q . f t . \end{aligned}$ of Drayton’s backyard.
::答案是A=452.16 sq.ft。圆环游泳池将覆盖德拉顿后院的452.16 sq.ft。

Example 2
::例2

Some students have formed a circle to play dodge ball. The radius of the circle is 21 feet. What is the area of their dodge ball circle?
::一些学生组成了一个圈来玩躲避球。圆的半径是21英尺。它们的躲避球圈的面积是多少?

First, write the formula.
::首先,写公式。

$\begin{aligned} A = π r^{2} \end{aligned}$

::阿 r2

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

$\begin{aligned} A = (3.14) (21)^{2} \end{aligned}$

::A=(3.14)(21)2

Then, following the order of operations, figure out the exponent first and then multiply.
::然后,按照操作的顺序,首先找出出价,然后乘以。

$\begin{aligned} \begin{array}{rcl} A & = & (3.14) (441) \\ A & = & 1, 384.74 s q . f t . \end{array} \end{aligned}$

::A=(3.14)(441)A=1 384.74 sq.ft。

The answer is $\begin{aligned} A = 1, 384.74 s q . f t \end{aligned}$ .
::答案是A=1 384.74 sq.ft。

Example 3
::例3

Find the area of a circle with a radius of 9 inches.
::查找圆形区域,半径为9英寸。

First, write the formula.
::首先,写公式。

$\begin{aligned} A = π r^{2} \end{aligned}$

::阿 r2

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

$\begin{aligned} A = (3.14) (9)^{2} \end{aligned}$

::A=(3.14)(9)2

Then, following the order of operations, figure out the exponent first and then multiply.
::然后,按照操作的顺序,首先找出出价,然后乘以。

$\begin{aligned} \begin{array}{rcl} A & = & (3.14) (81) \\ A & = & 254.34 s q . i n \end{array} \end{aligned}$

::A=(3.14)(81)A=254.34 sq.in

The answer is $\begin{aligned} A = 254.34 s q . i n \end{aligned}$ .
::答案是A=254.34 sq.in。

Example 4
::例4

Find the area of a circle with a radius of 11 inches.
::找到圆的圆区域,半径为11英寸。

First, write the formula.
::首先,写公式。

$\begin{aligned} A = π r^{2} \end{aligned}$

::阿 r2

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

$\begin{aligned} A = (3.14) (11)^{2} \end{aligned}$

::A=(3.14)(11)2

Then, following the order of operations, figure out the exponent first and then multiply.
::然后,按照操作的顺序,首先找出出价,然后乘以。

$\begin{aligned} \begin{array}{rcl} A & = & (3.14) (121) \\ A & = & 379.94 s q . i n . \end{array} \end{aligned}$

::A=(3.14)(121)A=379.94 sq.in。

The answer is $\begin{aligned} A = 379.94 s q . i n \end{aligned}$ .
::答案是A=379.94 sq.in。

Example 5
::例5

Find the area of a circle that has a diameter of 8 feet.
::找到一个直径为8英尺的圆形区域。

First, recognize that you have been given a diameter and divide by 2 to get the radius.
::首先, 承认您被赋予直径, 并用 2 来获得半径。

$\begin{aligned} \begin{array}{rcl} r & = & \frac{d}{2} \\ r & = & \frac{8}{2} \\ r & = & 4 feet \end{array} \end{aligned}$

::= rd2r=82r=4英尺

Next, substitute this value, along with pi, into the formula for the area of a circle.
::接下来,将此值与 pi 一起替换为圆区域公式。

$\begin{aligned} A = π r^{2} \end{aligned}$

::阿 r2

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

$\begin{aligned} A = (3.14) (4)^{2} \end{aligned}$

::A=(3.14)(4)2

Then, following the order of operations, figure out the exponent first and then multiply.
::然后,按照操作的顺序,首先找出出价,然后乘以。

$\begin{aligned} \begin{array}{rcl} A & = & (3.14) (16) \\ A & = & 50.24 s q . f t . \end{array} \end{aligned}$

::A=(3.14)(16)A=50.24 sq.ft。

The answer is $\begin{aligned} A = 50.24 s q . f t \end{aligned}$ .
::答案是A=50.24 sq.ft。

Review
::回顾

Find the area of each circle given the radius or diameter. Use 3.14 for the value $\begin{aligned} π \end{aligned}$ and round your answer to the nearest hundredths place where needed.
::查找每个圆的面积, 给其半径或直径。值为 ° 时使用 3. 14 , 并按需要将您的回答绕到最接近的百位位置。

$\begin{aligned} r = 3 i n \end{aligned}$
::r=3 英寸

$\begin{aligned} r = 5 i n \end{aligned}$
::r=5 英寸

$\begin{aligned} r = 4 f t \end{aligned}$
::r=4英尺

$\begin{aligned} r = 7 m \end{aligned}$
::rm=7米

$\begin{aligned} r = 6 c m \end{aligned}$
::r=6厘米

$\begin{aligned} r = 3.5 i n \end{aligned}$
::r=3.5 英寸

$\begin{aligned} d = 16 i n \end{aligned}$
::d=16 英寸

$\begin{aligned} d = 14 c m \end{aligned}$
::d=14 厘米

$\begin{aligned} d = 20 i n \end{aligned}$
::d=20 英寸

$\begin{aligned} d = 15 m \end{aligned}$
::d=15米

$\begin{aligned} d = 22 c m \end{aligned}$
::d=22厘米 d=22厘米

$\begin{aligned} d = 24 m m \end{aligned}$
::d=24毫米

$\begin{aligned} d = 48 i n \end{aligned}$
::d=48 英寸

$\begin{aligned} r = 16.5 i n \end{aligned}$
::r=16.5英寸

$\begin{aligned} r = 25.75 i n \end{aligned}$
::r=25.75英寸

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。

Resources
::资源

Section outline

General

圆圆区域

Finding the Area of a Circle ::查找圆圆区域

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)

Resources ::资源

Finding the Area of a Circle
::查找圆圆区域

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)

Resources
::资源