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The geometric meaning of double integral is volume, but double integral can produce negative number,
What is the geometric meaning of the mean value theorem of double integral?
In a curved top cylinder expressed by a binary function, there must be a point between the highest point and the lowest point, through which a plane parallel to the bottom can be made, and the volume of the cylinder formed by cutting the side of the curved top cylinder is equal to that of the original curved top cylinder
The application of surface area, volume and volume
1. A cuboid goldfish tank without cover is 8 decimeters long, 6 decimeters wide and 7 decimeters high. How many square decimeters of glass is needed to make the tank? 2. A cuboid iron block is 10 decimeters long, 5 decimeters wide and 4 decimeters high. Each cubic decimeter iron block weighs 7.8 kg. How many kilograms does this iron block weigh? 3. A cuboid iron sheet ventilation pipe is 2 meters long and its cross section is a cube with a side length of 10 cm, How much square centimeter iron sheet does it need to make this section of ventilation pipe? 4. Weld a 48 centimeter iron wire into a cuboid frame. The cuboid is 5 centimeter long and 4 centimeter wide. How high is it? 5. There is a long cuboid with a bottom area of 300 square centimeter and a height of 10 centimeter, which contains 5 centimeter deep water. Now immerse a stone in the water, The water rose 2 cm. What's the volume of this stone?
Application of volume and surface area
Use three cubes whose edges are all 0.8 decimeters long to form a cuboid. What is the volume and surface grid of the cuboid?
536 cubic decimeter
Table: 4.48 square decimeters
On the application of volume in the fifth grade of primary school
A piece of iron wire is 96 cm long, which is made into a cuboid frame. The length of the frame is three times the height, and the width is two times the height. Paste white paper on the outside of the frame. What is the volume of the cuboid model?
If the height is x, the length is 3x and the width is 2x,
6X*4=96,
X=4
V = x * 2x * 3x = 384 CC
On the application of square volume in the fifth grade of primary school
One cubic decimeter iron weighs 7.8 kg. There is a rectangular iron block with a square bottom, which weighs 93.6 kg. It is known that the side length of the square is 20 cm. How long is the iron block?
Because volume = the weight of the object divided by the weight of the unit volume
So 93.6 divided by 7.8 = 12 decimeters;
Because the cuboid volume = length * width * height, but the cuboid ground is a cube
So 12 divided by (2 * 2)
=12 divided by 4
=3 decimeters
=30 cm
By hand
On the application of rectangular volume in grade five of primary school?
1. A pool is 12 meters long, 5 meters wide and 4 meters deep. There are two water inlet pipes a and B to inject water into the pool at the same time. The water inlet of pipe a is 9 cubic meters per hour, and that of pipe B is 6 cubic meters per hour. After a few hours, the depth of the pool is 3 meters?
2. The owner of the fruit shop buys 200 kg of apples at the same price, and then divides them into high-quality apples and ordinary apples. The price of high-quality apples is 2 yuan higher than the purchase price, while the price of ordinary apples is 1.2 yuan lower than the purchase price. After these apples are sold out, they make a profit of 208 yuan. How many kg of high-quality apples are there?
1. The water depth of the pool is 3 meters, and its volume is 3 meters
V = 12 * 5 * 3 = 180 (M2)
Let the water depth of the pool be 3 meters after X hours
(9+6)*x=180
15*x=180
x=12
A: after 12 hours, the depth of the pool will be 3 meters
2. If the quality apple has x kg, the average Apple has 200-x kg
2*x-1.2*(200-x)=208
3.2x=448
x=140
A: there are 140 kg of high quality apples
The boss is very kind
Surface z = (x ^ 3-3axy + y ^ 3) / A ^ 2, tangent and normal plane equation at point P (a, a, - a)
Z to x partial derivative: ZX = (3x ^ 2-3ay) / (a ^ 2)
Partial derivative of Z to Y: ZY = (- 3ax + 3Y ^ 2) / (a ^ 2)
Normal vector: n = (ZX, ZY, - 1), tangent: (x-a) / ZX = (Y-A) / ZY = (Z + a) / (- 1)
Normal plane equation: ZX (x-a) + ZY (Y-A) - (Z + a) = 0
As shown in Figure 3, in the plane rectangular coordinate system, we know that the vertex coordinates of the triangle ABC are a (- 2,0), B (1,2), C (2, - 1) respectively to find the area of the triangle ABC
fast
AB=√13
BC=√10
AC=√17
With Heron formula,
The area of ABC is 5.5
Δ ABC is divided into two parts by the line segment De, Δ BDE and quadrilateral ACDE. The area of Δ BDE is a fraction of the area of quadrilateral
If △ ABC is divided into △ BDE and quadrilateral ACDE by segment De, ad = 6 dB = 2 be = 3 EC = 4, the area of △ BDE is a fraction of the area of quadrilateral
If D and E are the midpoint of AB and BC respectively, then s ⊿ BDE = (1 / 4) s ⊿ ABCs ⊿ BDE / S (deac) = (1 / 4) / (1-1 / 4) = 1 / 3. If BD / DA = k, be / EK = h. then s ⊿ BDE = [KH / [(1 + k) (1 + H)]] s ⊿ ABCs ⊿ BDE / S (deac) = [KH / [(1 + k) (1 + H)] / [1 -
RELATED INFORMATIONS
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