第二单元

How big are ice cream containers -- cylinders and cones

二 冰淇淋盒有多大——圆柱和圆锥

What questions can you ask?

你能提出什么问题？

Cooperative exploration

合作探索

What shape is the question on the left? What are their characteristics?

1. 左边的问题是什么形状的？它们有哪些特征？

The object on the left is cylindrical. What are the characteristics of a cylinder?

左边的物体是圆柱形的。圆柱有哪些特征呢？

The top and bottom sides of a cylinder are round and of the same size.

圆柱的上、下两个面都是圆，并且大小一样。

A cylinder has a curved surface.

圆柱有一个曲面。

The top and bottom sides of a cylinder are called the bottom, and the surfaces surrounding the cylinder are called the sides. The distance between the two bases is called height.

圆柱的上、下两个面叫作底面，围成圆柱的曲面叫作侧面。两个底面之间的距离叫作高。

2. What shape is the object on the right? What are their characteristics?

2. 右边的物体是什么形状的？它们有哪些特征？

The object on the right is conical.

右边的物体是圆锥形的。

What are the characteristics of a cone?

圆锥有哪些特征呢？

I find that the base of a cone is round.

我发现圆锥的底面是圆形的。

A cone has a curved surface.

圆锥有一个曲面。

The base of a taper is a circle, the flank of it is a curved surface. The distance from the apex of the cone to the center of the circle is the height of the cone.

圆锥的底面是一个圆，圆锥的侧面是一个曲面。从圆锥的顶点到底面圆心的距离是圆锥的高。

Lesson 2

Cylinder:   height 3dm  bottom  2dm

圆柱体：   高3dm      底面2dm

What questions can you ask?

你能提出什么问题？

Cooperative exploration

合作探索

1. How much cardboard is the minimum required to make such a cylindrical paper tube?

1. 做一个这样的圆柱形纸筒，至少需要多少纸板？

How much cardboard is needed, that is, find the surface area of the cylindrical paper tube.

求需要多少纸板，也就是求圆柱形纸筒的表面积。

I found that the area of the sides of the cylinder plus the area of the two bases is the surface area of the cylinder.

我发现圆柱的侧面积加上两个底面的面积就是圆柱的表面积。

The side area of a cylinder is equal to the perimeter of the base × the height

圆柱的侧面积＝底面周长×高

I'll figure out how many pieces of cardboard I need to make a cylinder.

我会求做圆柱形纸筒需要多少个纸板了。

Lesson 3

Cylinder: Height 20cm  Bottom  12cm

圆柱体： 高    20cm  底面     12cm

Cone:   height 10cm  Bottom  6cm

圆锥体：高     10cm  底面 6cm

What questions can you ask?

你能提出什么问题？

Cooperative exploration

合作探索

What is the volume of the cylindrical box in cubic centimeters?

1. 圆柱形包装盒的体积是多少立方厘米？

How do you find the volume of a cylinder?

怎样求圆柱的体积呢？

I know that the formula for the area of a circle is to convert a circle into an approximate rectangle.

我知道圆的面积公式是把圆转化成近似的长方形。

I suppose the formula for the volume of a cylinder may have been derived by converting the cylinder into a cuboid.

我猜想圆柱的体积公式可能是把圆柱转化成长方体来推导的。

How to convert a cylinder into a cuboid?

怎样把圆柱转化成长方体呢？

The more equal copies you have, the closer the cube is to a cuboid.

等分的份数越多，拼成的立体图形就越接近长方体。

What is the relationship between the finished cuboid and the original cylinder?

拼成后的长方体与原来的圆柱有怎样的关系？

The volume of the finished cuboid is equal to the volume of the original cylinder.

拼成后的长方体的体积等于原来圆柱的体积。

The volume of a cuboid is equal to  the area of the base times the height

长方体的体积＝底面积×高

The volume of the cylinder is equal to the area of the base times the height

圆柱的体积 ＝底面积× 高

V＝Sh

Base area:Three point one four times the square of the quotient of twelve divided by two is equal to one hundred and thirteen point zero four square centimeters.

底面积： 3.14×(12÷2)2＝113.04(cm2)

Volume: one hundred and thirteen point zero four times twenty equals to two thousand two hundred and sixty point eight  cubic centimeters.

体积：113.04×20＝2260.8(cm3)

A: The volume of the cylindrical box is two thousand two hundred and sixty point eight  cubic centimeters .

答：圆柱形包装盒的体积是2260.8 cm3。

2. What is the volume of the conical packing box in cubic centimeters?

2. 圆锥形包装盒的体积是多是立方厘米？

How do you find the volume of a cone?

怎样求圆锥的体积呢？

Let's do an experiment.

我们来做个试验把。

Experiments show that the volume of a cone is one third of that of a cylinder with base and height equal to it.

有实验得知：圆锥的体积等于与它等底等高的圆柱体积的三分之一。

The volume of the cone equals to  the area of the base times the height times one third

圆锥的体积 ＝底面积 ×高×1/3

V＝1/3Sh

Base area: three point one four times the square of the quotient of six divided by two equals to twenty eight point twenty six square centimeters.