Questions about the volume or surface area of a rectangular cube

First question. The volume of the cube is large when the surface area of the cube and the cuboid are equal;

xy+yz+xz>=3(xy*yz*xz)^(1/3)=(x*y*z)^(2/3)

When x=y=z, x*y*z obtains the maximum value.

That is, the cube is the largest in size.

Second question. With the same volume of the cube and the box, the box has a large surface area.

s=2v(1/x+1/y+1/z)>=6v(1/v)^(1/3)=6v^(2/3)

Same as above.

The third question. In the case of the same edge length and the same length of the cube and the cuboid, the surface area of the cuboid is still large and the surface area of the cube is still large?

There is no comparison between surface area and volume!

With the same edge length and the same length of the cube and the cuboid, the surface area of the cube is greater than the surface area of the box.

xy+yz+xz=[(xy+yz+xz)+2(xy+yz+xz)]/3<=[(x^2+y^2)/2+(y^2+z^2)/2+(x^2+z^2)/2+(2xy+2yz+2xz)]/3

x+y+z)^2/3

With the same edge length and the same length of the cube and the cuboid, the volume of the cube is greater than the surface area of the box.

x*y*z<=[(x+y+z)/3]^3

If this is a fill-in-the-blank or primary school student, it is recommended that the landlord use a simple enumeration method, give a practical example, you can get the answer, if you are a middle school student can remember like this, under the same conditions, the utilization rate of the length of the circle is the highest, and the square is compared with the rectangle, and the utilization rate of the length of the square is high. If you are a high school student, you can prove it with theorems and inequalities. For example, there is also a regular octagon with a higher utilization rate than a regular hexagon pair, and a regular hexagon with a higher utilization rate than a regular quadrilateral pair, that is, a larger area with the same circumference.

The cube is large, the surface area is large in the cuboid, and the edge length is the same, both are cube size

The surface area of the box and cube is as follows:

Cube surface area formula: s=6 (edge length, edge length), cuboid surface area formula: s=(length, width, length, height, width, height) 2. The sum of the areas outside all the solid figures is called its surface area.

A three-dimensional figure enclosed by six rectangles (in special cases, two opposite faces are squares) is called a cuboid. The cube is also a special cuboid.

A box's enclosed three-dimensional shape enclosed by six rectangles is called a cuboid, and the opposite side of any one of the sides of the cuboid is exactly the same as it.

A three-dimensional figure surrounded by six identical squares is called a cube. A straight parallel six-sided body with a square side and bottom surface is called a cube, that is, a hexahedron with equal edges and lengths, also known as "cube" and "regular hexahedron".

Cubes are special cuboids. The volume of the cube (or the volume of the cube) = edge length edge length edge length; Let the edge length of a cube be a, then its volume is: v=a a a or equal to a.

The hexahedron is a special kind of cuboid, and the similarity between the cuboid and the cube is that they both have 8 vertices, 6 faces, and 12 edges.

The difference between cuboid and cube is the same as that of the joint attack Pena system:

A cuboid is not necessarily a cube, but he includes a cube; A cube is a special type of cuboid.

From the characteristics of the cuboid and the cube nucleus, it can be seen that both the cuboid and the cube are composed of 6 faces, with 8 vertices and 12 edges.

A box is made up of six faces, the opposite faces are equal in area, and two of the faces may be square. The cube is a straight parallelepiped with both sides and bottom squares, that is, a hexahedron with equal edges and lengths, all 6 sides of the cube are equal, and all 12 edges are equal.

The dynamic definition of a hexahedron is a three-dimensional figure obtained by translating the side length of a square perpendicular to the face on which the square is located.

1) The surface area of the cuboid is a lost limb:

square decimeter) The volume of the box:

5 cubic decimeters).

2) The surface area of the box:

66 (square starvation rice).

The volume of the box: Chada.

4 3 3 = 36 (cubic meters).

Summary. Cube surface area = 6x side length x side length.

Hello about the surface area of the cuboid and the cube, don't see the question? Can I upload it?

To do this kind of question, you must first master their surface area for a total of ten days, and the surface area formula.

It's just that I don't know how to calculate the surface area and volume, it's the cuboid and the cube.

That's right, it's the formula.

Box surface area formula = 2x (length x width + length x height + width x height) cube surface area = 6x side length x side length.

The box has 6 faces, and the opposite 2 faces are the same, mmmm.

The 6 faces of the cube are the same.

Good. How do you calculate the volume?

Rectangle volume = length x width x height.

Cube volume = side length 3

Square volume = side length x side length x side length.

Decimeter = meter.

s=2*(sqm.)

2. s=2*(15+15*square decimeter.)

3. S = square meters.

36* kg.

Table imitation search area area = 2x (length x width x height x length) of the first large state of the source.

16 square meters.

54 square decimeters. Kilogram.

Surface area of the box = (length x width + length x height + width x height) x 2

The surface area of the cube = edge length x edge length x 6

Let the edge length be a

then the cube. Surface area 6a 2

Volume A 3 is set to the edge lengths of ABC rule.

The surface area is 2AB+2AC+2BC

The volume is ABC

What grade are you, little classmate, so you won't just look for it from textbooks.

1. Surface area: 9 2 10 2 8 2 54 (square centimeters).

2, along the long cut 3 knives to add 6 width and height of the surface, along the width of the cut 4 knives to increase 8 length and height of the surface, along the height cut 5 knives to add 10 length and width of the surface, plus the original 2 width and height, length and height, length and width of the surface, so, the sum of the surface area is:

8 wide and high surfaces 10 long and high surfaces 12 long and wide surfaces 8 1 1 1 10 1 1 1 1 1 30 (square meters).

3. The sum of length, width and height is: 64 4 16 (decimeters), the smaller the difference between length, width and height, the larger the volume. Because the rectangular iron sheet can be equipped with a cube wooden block with a edge length of 1 decimeter as much as possible, the length, width and height should be taken as a whole decimeter.

16＝5＋5＋6。Therefore, the length, width, and height of the made cuboid with a lid are 6 decimeters, 5 decimeters, and 5 decimeters, respectively. Its surface area is:

2 5 5 4 6 5 50 120 170 (square decimeter).

1.Surface area = 2 (10 + 8 + 9) = 54 square centimeters = 6 + 24

30 square decimeters.

3.Edge length = 64 12 = 16 3 dm.

6 (16 3) = 512 3 square decimeters.

1.The projection area (upper, lower, left, right, front, and back) from six different directions is , so the sum is 9+9+8+8+10+10=54, that is, the surface area of this three-dimensional figure is 54 square centimeters.

2.The answer is (1 4 * 1 5 + 1 5 * 1 6 + 1 4 * 1 6) * 2 * 120 = 30 (square meters).

3.Use a*b*c less than or equal to (a+b+c) 3 cubes, because if there is a cuboid iron sheet with a lid that can be made of 1 decimeter long cube wood block as much as possible, a, b, c are taken. So (5*5+5*6+5*6)*2=170 square decimeters.

1.Increase in surface area = 84 6 2 = 28 square centimeters.

2.Height = 500 4 7 = 125 7 cm chain reed.

Volume = 125 7 7 7 = 875 cubic centimeters.

3.Volume = root number (3 6 8) = 12

Cm. Edge length = 3 cm.

In the same way, the other two long-edged jujube hailstones are 4 cm and 5 cm respectively.

Volume sum = 3 3 3 + 4 4 4 + 5 5 5 = 216 cubic centimeters.

6 = 14, so the surface area increases by 14 + 14 = 28 square centimeters.

2. Height = 500 (7 4) = 125 7 cm.

So its volume is 7 7 125 7 = 875 cubic centimeters.

So its volume is 12 (because 12 12 = 144) 6 = 9, so the surface area is 54 square centimeters with an edge length = 3 centimeters.

96 6 = 16, so the edge length of the surface area of 96 square centimeters = 4 centimeters.

150 6 = 25, so the surface area is 150 square centimeters of edge length = 5 centimeters.

Therefore, the volume of this large cube hand is 3*3*3+4*4*4+5*5*5*5=27+64+125=216 cubic meters.

Have fun!

1.Let the side length of the square be a. So it can be listed.