10.8圆的面积
章节大纲
-
Debra is looking for a table to go in a small breakfast nook in her house. In order to get a table and two chairs in the breakfast nook, the table must be smaller than 2 square feet in area . Debra sees a table she likes. The table has a diameter of 28 inches. How can Debra figure out if the table is small enough to fit in the breakfast nook?
::Debra正在寻找一张桌子,在她家的一个小早餐之屋里。为了在早餐之屋里找到一张桌子和两张椅子,桌子必须小于地区两平方英尺。Debra看到一张她喜欢的桌子。桌子直径28英寸。Debra如何能弄清楚桌子是否小到足以适应早餐之屋?In this concept, you will learn to find areas of circles given the radius or the diameter.
::在这个概念中,根据半径或直径,您将学会寻找圆圈区域。Finding Area of Circles
::查找圆圆区域The inside of a circle is called the area of the circle. The area is the surface or space inside the circle.
::圆的内侧称为圆的区域。区域是圆内的表面或空间。In this picture, the area of the circle is yellow. As you can see, it is all the space inside the circle.
::在此图片中, 圆的面积是黄色的。 正如您所看到的, 它就是圆内的全部空间 。To figure out the area of a circle, you will need a couple of different measurements. The first one is pi . You will need to use the numerical value for pi , or 3.14, to represent the ratio between the diameter and the .
::要找出圆的面积, 您需要几个不同的测量。 第一个是 pi 。 您需要使用 pi 的数值值, 或者 3. 14 来表示直径和 直径之间的比 。The next measurement you need to use is the radius , which is the distance from the center of a circle to the edge , or half of the circle’s diameter.
::您需要使用的下一个测量方法是半径, 也就是圆的中心到边缘的距离, 或者圆的直径的一半。To calculate the area of a circle, multiply the radius squared (multiplied by itself) by pi (3.14). Here is the formula.
::要计算圆的面积,请将半径平方乘以 pi (3.14) 。 这是公式 。Let’s try an example.
::让我们以身作则。Find the area of the circle.
::查找圆圈的区域 。First, substitute the given information into the formula.
::首先,将给定信息替换为公式。Next, multiply.
::下一个,乘数。Notice that area is measured in square units .
::注意区域以平方单位计量。If you have been given the diameter and not the radius, you can still figure out the area of the circle.
::如果给定了直径而不是半径,您仍然可以找出圆的面积。Start by dividing the diameter in half since the radius is one-half the measure of the diameter then use the formula and solve for area.
::开始时将直径除以半, 因为半径是直径的半径, 然后使用公式并解决区域 。Find the area of the circle with a diameter of 6 inches.
::查找圆的直径为6英寸的区域。First, divide the diameter in half to find the radius.
::首先,将直径除以一半以找到半径。
::6 2 = 3 英寸 = 半径Next, substitute the given values into the formula and solve for the area of the circle.
::接下来,将给定值替换为公式,并解决圆区域。Examples
::实例Example 1
::例1Earlier, you were given a problem about Debra and the table she wants for her breakfast nook.
::早些时候,你得到一个问题 关于黛博拉 和她想要的餐桌 她的早餐 Nook。Debra’s husband measured the space in the breakfast nook and told her the table has to be less than 2 square feet to fit comfortably in the nook. The table Debra likes has a diameter of 28 inches. Debra needs to use the area of a circle formula to find the area of the table.
::Debra的丈夫测量了早餐之洞的空间,并告诉她,桌子必须小于2平方英尺才能舒适地适应。 Debra喜欢的桌子直径为28英寸。 Debra需要使用圆形公式的面积来找到桌子的面积。First, she should divide the diameter in half to find the radius.
::首先,她应该把直径除以一半 才能找到半径The radius is 14 inches.
::半径14英寸Next, substitute the given values into the formula.
::接下来,将给定值替换为公式。Next, evaluate the exponent and multiply.
::下一步,评价指数和乘法。The area of the table is 615.44 square inches.
::表格面积为615.44平方英寸。Then, to find out if the table will fit in the nook, convert the 2 square feet into inches.
::然后,看看桌子是否合适 将2平方英尺转换成英寸The table must be smaller than 576 square inches to fit in the space. The table is too big.
::桌子必须小于576平方英寸才能适应空间。桌子太大了。Example 2
::例2The diameter of a circle is 13 feet. What is the area of the circle?
::圆的直径是13英尺。圆的面积是多少?First, divide the diameter in half to find the radius.
::首先,将直径除以一半以找到半径。
::132=6.5英尺The radius is 6.5 feet.
::半径是6.5英尺Next, substitute the given values into the formula and solve for the area of the circle.
::接下来,将给定值替换为公式,并解决圆区域。Then, round up the nearest hundredth.
::然后把最近的一百个集合起来The answer is 132.67 sq. feet.
::答案是132.67平方英尺Example 3
::例3Find the area given the radius.
::查找给定半径的区域 。First, substitute the given information into the formula.
::首先,将给定信息替换为公式。Next, evaluate the exponent and multiply.
::下一步,评价指数和乘法。The answer is .
::答案是452.16cm 2。Example 4
::例4Find the area given the radius.
::查找给定半径的区域 。First, substitute the given information into the formula.
::首先,将给定信息替换为公式。Next, evaluate the exponent and multiply.
::下一步,评价指数和乘法。The answer is .
::答案是1017.36cm 2。Example 5
::例5Find the area given the diameter.
::查找给定直径的区域 。First, divide the diameter in half to find the radius.
::首先,将直径除以一半以找到半径。The radius is 7 inches.
::半径是7英寸Next, substitute the given values into the formula.
::接下来,将给定值替换为公式。Next, evaluate the exponent and multiply.
::下一步,评价指数和乘法。The answer is .
::答案是153.86 f t 2。Review
::回顾Find the area of the following circles given the radius. Use the value approximated value 3.14 for the number
::根据半径查找以下圆圈的面积。使用大约值3.14的数值表示编号 + 。-
::r = 4 i n 。 -
::r = 5厘米。 -
::r = 8 i n 。 -
::r = 2厘米。 -
::r = 7米。 -
::r = 9 i n 。 -
::r = 10 f t. -
::r = 11厘米。 -
::r = 20英尺吨。 -
::r = 30米i.
Find the area of the following circles given the diameter. Use the value approximated value 3.14 for the number
::根据直径查找以下圆圈的面积。使用数值大约为3.14的数值表示 。-
::d = 10 i n 。 -
::d = 12米。 -
::d = 14厘米。 -
::d = 16 f t. -
::d = 18 i n 。 -
::d = 22英尺吨。 -
::d = 24厘米。 -
::d = 28米。 -
::d = 30米。 -
::d = 36 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 。Resources
::资源
-