How to make the largest cylinder from a sheet of A4 paper 5

In order to facilitate the calculation, a box with a length of 18cm and a width of 12cm was designed as the query object.

1. Form a cylinder on the long and short sides of the cuboid respectively.

2. Calculate the volume of two cylinders separately;

3. In contrast, the volume of the cylinder obtained along the long side of the cuboid is larger;

4. Study what happens when you cut a cuboid and then wrap it around a cylinder. Calculate their volumes separately;

5. Compare the dimensions of all closed cylinders separately. In all closure methods, the maximum cylinder volume is obtained by cutting the box in half along the short side and then rolling it horizontally.

Summary: As you can see from the above, the roller is made of A4 paper.

Made-up. If the paper is not cut, the long side of the A4 paper is used as the bottom of the roller, and the short side is used as the height of the roller. At this time, the volume of the cylinder is maximum. When cutting paper, cut the box in half along the short side and roll it horizontally for maximum volume.

A4 paper size: 21cm*, first cut a circle with a diameter of 21cm, because all cones are rolled up with circles. Then the radius of the circle is, indicating that the conical bus bar is set to be the height of the cone x and the radius of the bottom surface is y, then x 2 + y 2 = and y 2 = cone volume:

Pi xy 2) 3=(Pai 3)* (find its maximum value, you can find the derivative: the derivative is, when the formula is 0, x=negative value rounded off) then vmax = cubic centimeter This is not sealed, the seal is too complicated to be foolish to calculate.

If you don't consider the situation that the upper and lower bottom is empty, you can roll it up directly. The A4 paper length is used as the circumference of the upper and lower bottom of the cylinder.

Is volume the same as surface area.

1. Take 4 sheets of A4 paper (if there is no A4 paper, tear 4 sheets of paper from your homework book) 2. Take out a piece of A4 paper, overlap the two short sides, bond them together, and enclose them into a cylinder as the side of the cylinder; Glue the cylinder vertically to another sheet of A4 paper, cut off the bottom surface of the cylinder as the bottom surface of the cylinder, and make the top of the cylinder in the same way. A cylinder is done.

3. Take out 1 piece of A4 paper, take the midpoint of a long side, connect the two ends of the other long side to form a triangle, cut off the part other than the triangle, and overlap the two ends of the bottom edge of the triangle and bond them together as the side of the cone. Take another piece of A4 paper and lay it flat, then stick the side of the cone vertically on the A4 paper, and cut off the part outside the bottom surface of the cone. A cone is done.

4.Because the cylinder and the cone are all made of A4 paper with a long side as the bottom circumference, and the short side of A4 paper as the height, Zheng Xing accompanies them to be equal in height.

The long side of the A4 paper is used to make the bottom of the cylinder, and the short side is used to make the height of the cylinder, and the volume of the cylinder is the largest. The process of solving the problem is as follows:

For example, the volume formula of A4 paper is 210mm 297mm cylinder is: v s bottom h v= r h with the short side as the bottom, and the volume of the long side sitting high is: v =

The side of a cylinder is a curved surface, and the side of a cylinder is illustrated as a rectangle, square, or parallelogram of a cylinder where the two bottom faces are exactly the same two circular faces. The distance between the two bottom faces is the height of the cylinder.

The long side is the bottom, and the short side is high.

Because the radius is squared to enlarge.

To put it simply, the long side of the A4 paper is used to make the bottom of the cylinder, and the short side is used to make the height of the cylinder, and the volume of the cylinder is the largest.

The long side is the bottom, and the short side is high.

Because the radius is squared to enlarge.

In order to facilitate the calculation, we also designed a rectangle with a length of 18cm and a width of 12cm as **.

1. We enclose a cylinder along the long and short sides of the cuboid respectively;

2. Calculate the volume of these two cylinders separately;

3. After comparison, it is known that the volume of the cylinder enclosed along the long side of the cuboid is larger;

4. What will happen to the results of the cuboid after cutting the cuboid and then surrounding the cylinder, and calculate their volume separately;

5. Compare the size of all the enclosed cylinders respectively, and it can be obtained that the volume of the cylinder obtained by cutting the cuboid in half along the short side and then rolling horizontally in all the enclosure methods can be obtained.

From the above, it can be seen that if the cylinder is made with A4 paper, if the paper is not cut, the long side of the A4 paper is used to make the bottom of the cylinder, and the short side is used to make the height of the cylinder, and the volume of the cylinder is the largest; If the A4 paper is cut, the cuboid is cut in half along the short side and then rolled horizontally, resulting in the largest volume of the cylinder.

A4 paper is defined by ISO 216 of the International Organization for Standardization, with a specification of 21*, and most countries in the world use this international standard for paper sizes.

This standard was first incorporated into DIN (DIN 476) by the Weimar Republic in 1922, although some of these formats were developed in France during the same period, but have since been forgotten.

ISO 216 defines three groups of paper sizes: A, B, and C. Group C paper size is mainly used for envelopes.

To put it simply, the long side of the A4 paper is used to make the bottom of the cylinder, and the short side is used to make the height of the cylinder, and the volume of the cylinder is the largest.

If you don't consider the situation that the upper and lower bottom is empty, you can roll it up directly. The A4 paper length is used as the circumference of the upper and lower bottom of the cylinder.

Here's one way to do it::

1.Start by preparing 2 sheets of A4 paper. Fold one of the sheets in half from the middle and fold the middle halves in half again. After the last stop, the folded paper is glued together to form a rectangle.

2.For the other sheet, first fold it vertically in half. Next, fold it diagonally and cut it in the middle, taking care not to cut the ends completely. Finally, the paper is pulled apart to form a rectangle with a cross space in the middle.

3.Bend the first sheet of paper to the bottom of the cube and secure it with glue on the back. Next, the second sheet of paper is bent over the side walls of the cube and fixed with glue at the bottom and front.

Finally, attach the remaining top part to the top of the box and make it connect with the side walls and bottom.

4.Finally, a door or section can be cut at one end or side of the box, and the cover can be used to better show the inside of the box.

Through the above steps, we can successfully make a relatively large box. It is important to note that in the process of building a cuboid, we need to accurately measure the size and bending of each paper to ensure that their dimensions and angles match each other, and that they can be combined into a stable cuboid.

Although the size of A4 paper is relatively small, through clever folding and gluing, we can also create many interesting and useful three-dimensional shapes, which is one of the charms of handcrafting. <>

Here's how to make a cylinder out of paper:

1. To make a cylinder, first draw a circle on the paper, cut out two identical circles, and calculate the circumference of the circle (the length of the side view of the cylinder). Due to the thickness of the paper and the fact that it is pasted at the time of production, the length is a little longer when you see the side view. As for the height of the cylinder, you can decide for yourself.

2. Then according to the cut circle, adjust the size of the side of the cylinder and paste it into a cylinder.

3. Finally, glue two circles. To make a cone, first cut a large circle as the side. Start from any point on the circle, cut out the center of the circle, pull the two sides together to form a cone, paste the shape, put it on the paper to trace the ground, cut it and paste it.

Supplementary information: A cylinder is a three-dimensional shape formed by rotating the rectangle once on one side of the rectangle, and the volume of the cylinder is equal to the base area times the height.

In the same plane, there is a fixed line and a moving line, when this plane rotates around this fixed line, the surface formed by this moving line is called the rotating surface, this fixed line is called the axis of the rotating surface, and this moving line is called the bus bar of the rotating surface. If the bus is a straight line parallel to the axis, then the resulting rotating surface is called a cylindrical surface.

If the cylindrical surface is truncated by two planes perpendicular to the axis, then the geometry enclosed by the two sections and the cylindrical surface is called a straight cylinder, referred to as a cylinder. The cylinder, in turn, can be seen as the result of a rectangle rotating around one side of it.

Summary. Hello, your question has been seen and the answer is being sorted out for you.

Use a piece of A4 paper to make the largest cone, please ask everyone, do you know, do me a favor, thank you

Hello, your question has been seen and the answer is being sorted out for you.

Hello, because the cone is a fan after being disassembled from a bus bar in the bright and hidden hall, you can clean and change the midpoint of the long side of the A4 paper as the original center, and the width of the A4 paper is the radius, and then find the B and C points on the width of both sides and the D point on the long side of the opposite side, connect them into a fan shape and then cut them down, you can get a maximum fan.

You can also prepare two pens and one**, the length of ** and the width of the A4 paper is slightly longer to connect the two pens with **, after the A4 paper is fixed, one of the pens, fixed and split the finger at point A as shown in the figure above, and then pull and grind the moving line and draw an arc on the A4 paper with the known pen at the outer end, you can get a maximum fan.

Hope mine is helpful to you.

1. Take 4 sheets of A4 paper.

2. Take out a piece of A4 paper, overlap the two short sides, glue them together, and enclose them into a cylinder as the side of the cylinder; Glue the cylinder upright on another sheet of A4 paper, cut off the bottom surface of the cylinder as the bottom surface of the cylinder, and make the top of the cylinder in the same way. A cylinder is done.

3. Take out 1 piece of A4 paper, take the midpoint of a long side, connect the two ends of the other long side to form a triangle, cut off the part other than the triangle, and reunite the two ends of the bottom edge of the triangle together and bond them together as the side of the cone. Take another piece of A4 paper and lay it flat, then stick the side of the cone vertically on the A4 paper, and cut off the part of the outer fiber and filial piety outside the bottom surface of the cone. A cone is done.

4.Because the cylinder and the cone are both based on the long side of A4 paper as the bottom circumference and the short side of A4 paper as the height, they are equal in height at the bottom.