The perfect shape -- the circle 五 完美的图形——圆 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 Why are wheels round in design? 轮子为什么设计成圆形的呢？ Draw a circle and study it. 画一个圆，研究一下。 When drawing a circle, the fixed point is the center of the circle, which is usually denoted by the letter 0.The line segment connecting the center of the circle to any point on the circle is called the radius and is usually represented by the letter R.A line segment that passes through the center of a circle and both ends are on the circle is called a diameter and is usually denoted by the letter D. 画圆时，固定的点是圆心，圆心一般用字母0表示。连接圆心和圆上任意一点的线段叫做半径，一般用字母r表示。通过圆心并且两端都在圆上的线段叫做直径，一般用字母d表示。 Let's study the relationship between the diameter of a circle and its radius. 我们来研究一下圆的直径和半径的关系吧。 d equals to 2r r equals to d second d＝2r r＝d/2 What is the coloring part in the following figure? 下面图形中的涂色部分是什么图形？ The painted circles in the figure above are sectors. 上图各圆中涂色部分就是扇形。 The Angle whose vertex is at the center of the circle is called the central Angle, as shown on the right. 如右图，向∠1这样，顶点在圆心的角叫做圆心角。 Think about it. What does the size of the sector in the same circle have to do with? 想一想，同一个圆中，扇形的大小与什么有关？
Lesson 2 The Temple of Heaven is mainly composed of two altars: Circular Mound and Qi Valley (Hall of Prayer for Good Harvest). 天坛主要由圜丘和祁谷(祈年殿)两坛组成。 The Circular Mound Altar, commonly known as the Worship Terrace, has three floors. The diameter of the upper circle is 30 meters, and the diameter of the middle circle is 圜丘坛俗称祭天台，共有三层。上层圆台的直径是30米，中层直径是50米，下层直径是70米。 The top perimeter of the Hall of Prayer for Good Harvest is 100 meters. 祈年殿殿顶周长是100米。 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 1. How many meters is the perimeter of the upper circle of the worship platform? 1. 祭天台上层圆台的周长是多少米？ Measure the diameters and perimeters of several circles and see how they relate. 测量几个圆的直径和周长，看它们有什么关系。 What does the circumference of a circle have to do with its diameter? 圆的周长与直径有什么关系呢？ If the circumference of a circle is expressed in terms of C, can you write a formula for calculating the circumference of a circle? 如果用C表示圆的周长，你能写出圆周长的计算公式吗？ C = πd or C = 2πr C＝πd 或 C＝2πr I'll calculate the perimeter of the upper deck. 我会计算祭天台上层的周长了。 Three point fourteen times thirty equals to ninety four point two(meters) 3.14×30＝94.2(米) 2. What is the diameter of the top of the Hall of Prayer for Good Harvest? 2. 祈年殿殿顶的直径是多少米？ According to C = πd, and I'm going to write an equation to solve it. 根据C＝πd,我列方程解答。 Solution: Let the diameter of the top of the Hall of Prayer for Good Harvest be x meters. 解：设祈年殿殿顶的直径是x 米。 X times three point fourteen equals to one hundred X × 3.14＝100 Answer: The diameter of the roof of the Hall of Prayer for Good Harvest is about 31.85 meters. 答：祈年殿殿顶的直径是约是31.85米。
Lesson 3 The diameter of the circular center stage in the closing ceremony of the 2008 Beijing Olympic Games is 20 meters, including a circular lifting stage with a diameter of 1.6 meters. 2008年北京奥运会闭幕式圆形中心舞台的直径是20米，其中有一个直径是1.6米的圆形升降舞台。 What questions can you ask? 你能提出什么问题？ Cooperative exploration 合作探索 1. What is the area of center stage in square meters? 1. 中心舞台的面积是多少平方米？ The area of the center stage is the same thing as the area of the circle. 求中心舞台的面积也就是求圆的面积。 How do you find the area of a circle? 怎样求圆的面积呢？ You can study circles by turning them into shapes that you've already learned. 可以把圆转化成已经学过的图形来研究。 How does the rectangle relate to the original circle? 拼成的长方形与原来的圆形之间有怎样的关系？ If the area of a circle is represented by S, then the formula for calculating the area of a circle can be written as: 如果用S表示圆的面积，那么圆的面积计算公式可以写成： S＝πr2 The area of center stage is 314 square meters. 中心舞台的面积是314平方米。 What is the area of the figure below in square centimeters? 下面图形的面积是多少平方厘米？ This figure is a ring form. 这个图形是环形。 To find the area of the ring, you can subtract the area of the inner circle from the area of the outer circle. 求环形面积，可以用外圆面积减去内圆面积。 |
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