A rectangular piece of paper with a length of 30 cm and a width of 20 cm is rolled into a cylinder a

1) If the long side is curled, the radius of the cylinder is meters, and the volume is cubic meters.

2) If the wide side is curled, the radius of the cylinder is meters, and the volume is cubic meters.

There are two possibilities: 1, (30

Represents multiplication.

Find the radius first;

20 2 = 10 (cm).

in the area of the land counted;

10 10 square centimeters).

in the calculation of volume; 314 30 = 9420 (cubic centimeters).

1.Divide 30 by pi and divide by two to find the base radius, and multiply the square of the radius by pi and multiply it by 20.

2..Divide 20 by pi and divide by two to find the base radius, and multiply the square of the radius by pi and multiply by 30.

Radius; 20 2 = 10 (cm).

base area; 10 10 square centimeters).

Volume; 314 30 = 9420 (cubic centimeters).

Summary. If you roll a rectangle 30 cm long and 20 cm wide into a cylinder, then the height of the cylinder is equal to the width of the rectangle.

If you roll a rectangle 30 cm long and 20 cm wide into a cylinder, then the height of the cylinder is equal to the width of the rectangle.

So the height of the cylinder is equal to 20

Because the width of the rectangle is directly equal to the busbar of the cylinder.

And the circumference of the base surface of this cylinder is also equal to the length of this rectangle.

You can imagine the space.

This question tests the ability to think spatially about shapes, and it is recommended to study it by heart, as the later chapters will be more abstract.

The maximum circumference of the bottom surface is 20 centimeters.

You can use a rectangular piece of paper to roll it up, do you still use the equation? Because you flatten the cylinder, the circumference of the circle is the length of the original rectangle. Take a look at the red line in the image below.

1.When the height is 10 cm, the maximum base circumference is 20 cm.

2.When the height is 20 cm, the maximum circumference of the base surface is 10 cm.

Circumference: 20 cm 10 cm.

The height can be 20 cm or 10 cm.

There are two types of rolling, one horizontal and one vertical.

Supplementary answers! The bottom circle is 10 as the diameter, so r=5cm l = 2* *r=10 circumference is the length of the rectangle, 20cm

The surface area of the cylinder is equal to the area of the rectangle, so 20*10 is unchanged, when the height is 10, the bottom circumference is up to 20, and when the height is 20, the bottom circumference is up to 10

For a student like me who can't study, this question is very difficult.

When the height is 10, the bottom circumference is 20

20 in height, 10 in bottom circumference

Roll a rectangle of paper 20cm long and 10cm wide into a cylinder, when the height is 10cm, what is the maximum circumference of the underside?

A: The maximum circumference of the underside is 20cm.

Think: When the height is 10 cm, the width of the rectangle becomes the height of the cylinder, and the length becomes the circumference of the bottom surface of the cylinder.

There are two cases:

1. When the length of the rectangular paper is 20 cm as the bottom of the cylindrical paper tube, the circumference of the bottom surface of the cylindrical is 20cm, and the height is 15cm;

2. When the width of the rectangular paper is 15 cm as the bottom of the cylindrical paper tube, the circumference of the bottom surface of the cylindrical is 15cm, and the height is 20cm.

Analysis: From the characteristics of the cylinder, it can be seen that the side of the cylinder is a curved surface, and the side of the cylinder is a rectangle, square or parallelogram.

2 possibilities.

Bottom circumference = 20 cm.

Height = 15 cm.

or base circumference = 15 cm.

Height = 20 cm.

When the base circumference is 20, the height is 15. When the base circumference is 15, the height is 20.

The first possibility: when height = 20, base girth = 15

The second possibility: when height = 15, base circumference = 20

2 possibilities.

1. Use length to make the bottom circumference.

Bottom circumference = 20 cm.

Height = 15 cm.

2. Use width as the bottom perimeter.

Base circumference = 15 cm.

Height = 20 cm.

It is discussed in two cases. One is 15 and 20 and the other is 20 and 15

Roll a rectangular sheet of paper 20 cm long and 10 cm wide into a cylinder, with a maximum base circumference of 20 cm when the height is 10 cm, and a maximum of 10 cm when the height is 20 cm.

Volume: Take.

When the height is 10 cm:

Bottom circumference = 2 r = 20, then r = 10

v= r 2*h= (10) 2*10=1000 = cubic centimeter.

When the height is 20 cm:

Bottom circumference = 2 r = 10, then r = 5

v= r 2*h= (5) 2*20=500 = cubic centimeters.

Depending on how you roll, if you take the length as the bottom surface, the bottom circumference is 20 cm, the diameter is 20, and the area is calculated by yourself, if the width is the bottom surface, the bottom circumference is 15 cm, the diameter is 15, and the area is calculated by yourself.

Roll a rectangular piece of paper 30 cm long and 20 cm wide into a cylindrical core paper tube, and the bottom circumference of this paper tube and the height of the paper tube are 30 cm and 20 cm, or 20 cm and 30 cm

So the answer is

2 possibilities. The circumference of the underside takes which front = 20 cm.

Height = 15 cm slow beat.

Or. The length of the circumference of the bottom surface = 15 cm.

Height = 20 cm.