In the triangular pyramid a-bcd, the side edges AB, AC and AD are perpendicular. If the areas of △ ABC, △ ACD and △ ADB are √ 2 / 2, √ 3 / 2 and √ 5 / 2 respectively, what is the volume of the triangular pyramid?

Let AB = a, AC = B, ad = C;
The volume of triangular pyramid is s
ab/2=√2/2
bc/2=√3/2
ac/2=√5/2
S=(ab/2)*c/3=abc/6
The solution is s = √ 30 / 6
Note (equation solution): multiply the first three equations

If the bottom is a rhombic prism, its side edges are perpendicular to the bottom, and the length of the side edges is 5, the length of its diagonal is 9 and 15 respectively, then the side area of the prism is ()
A. 130B. 140C. 150D. 160

As shown in the figure, in abcd-a'b'c'd ', the two diagonals are a'c = 15cm, BD' = 9cm, and the side edges are AA '= DD' = 5cm. Both ∵ BDD 'and ∵ ACA' are right triangles. According to Pythagorean theorem, ac2 = 152-52 = 200, BD2 = 92-52 = 56, AC = 102, BD = 214 ∵ AC and BD are the two diagonals of diamond ABCD, and ∵ AC and BD are bisected vertically to divide the diamond into congruence According to the Pythagorean theorem, the length of the oblique side AB = 8. The side product of the prism s = 4 × 8 × 5 = 160

It is known that △ a ′ B ′ C ′ is an equilateral triangle with side length a, then the area of the original △ ABC is ()
A. 32a2B. 34a2C. 62a2D. 6a2

Intuitionistic graph △ a ′ B ′ C ′ is an equilateral triangle with side length a, so the area is 34a2. The relationship between the area of original graph and intuitionistic graph is s intuitionistic graph s original graph = 24, then the area of original △ ABC is 62a2, so C is selected

A mathematics problem of senior one about space geometry
If four balls with radius of 1 are tangent to each other, they are all in a big ball, and they are tangent to the big ball, what is the radius of the big ball?
Analysis: let the centers of four small balls be ⊙ 1, ⊙ 2, ⊙ 3, ⊙ 4 respectively. Then we can get the cube with the edge length of root 2, and we can cut the regular tetrahedron with the edge length of 2 ⊙ 1 ⊙ 2 ⊙ 3 ⊙ 4, ∵ the cube and the regular tetrahedron are circumscribed with the same ball, ∵ the diameter of circumscribed ball 2r1 = (root 3) * (root 2), that is R1 = (root 6) / 2, Ψ r = R1 + r = (radical 6) + 1
What I'm puzzled about is how to place the tetrahedron and cube. I'm not very good at spatial imagination. I hope some experts can explain it in detail. It's best to draw pictures. If your analysis is good, I will add 30-50 reward points,

This problem needs some spatial thinking
According to the known conditions, four equal spheres are tangent to each other, so their centers are connected to form a regular tetrahedron
So you can draw this tetrahedron on paper, and then you find that the center of their big circle can only be the center of the tetrahedron,
If the distance h from the vertex to the center is easy to find, the process will not be written as H = 6 ^ (1 / 2) / 2, which is the root of two sign 6 (I'm sure you know)
So the radius of the big circle is H + 1
What questions do you have in the future^_^

Who has high school compulsory 2 space geometry surface area volume formula to complete
All cylinders, cones, billiards

Volume formula of surface area of space geometry: volume formula of cylinder: volume = bottom area × height, if h represents the height of cylinder, then cylinder = s bottom × h volume formula of cuboid: volume = length × width × height, if a, B and C represent the length, width and height of cuboid respectively, then cuboid volume formula

Surface area and volume of a space geometry
The surface area of the ball is doubled. How many times is the volume of the ball?

The surface area is proportional to the square of the radius of the ball
If the surface area is increased to 2 times of the original, the radius will be increased by √ 2 times
The volume is proportional to the third power of the radius
So the volume is enlarged (√ 2) & # 179; = 2 √ 2 times

The surface area and volume of mathematics space geometry in Senior Two
1. There is a cylindrical glass with a bottom diameter of 20cm and a part of water. There is a conical plumb with a bottom diameter of 6cm and a height of 20cm in the water. When the plumb is taken out of the water, how many centimeters will the water in the glass drop? (π = 3.14)
2. It is known that the side length of the square on the bottom of a regular pyramid is 4cm, and the angle between the height and the oblique height is 30 degrees. The side area and the surface area (unit: CM & sup2;) of a regular pyramid are calculated
3. The height of a cone is equal to the radius of its bottom, so is the height of an inscribed cylinder. Find the ratio of the surface area of a cylinder to that of a cone

1、（3.14*3*3*20/3）/(3.14*10*10)
2. The length of the square on the bottom of the regular pyramid is 4cm, and the angle between the height and the oblique height is 30 degrees,
Oblique height L = 4 / (2 * sin30 °) = 4;
The side area of regular pyramid S1 = (4 * 4 / 2) * 4 = 32
Surface area s = S1 + 4 * 4 = 48
3. The height h of a cone is equal to the radius r of its bottom, and the height l of its inscribed cylinder is equal to the radius r of its bottom;
The surface area of cylinder S1 = pi * r * r * 2 + pi * 2 * r * l = 4 * pi * r * r
The surface area of cone s = pi * r * r + 2 * pi * r * r / 2 = 2 * pi * r * r
The ratio of surface area of cylinder to that of cone (2rr / 4rr) = 1 / 8

Calculate the surface area and volume of the figure below

The surface area of cuboid is 2 × (5 × 4 + 5 × 10 + 4 × 10) = 2 × (20 + 50 + 40) = 2 × 110 = 220 (square centimeter); the volume of cuboid is 5 × 4 × 10 = 200 (cubic centimeter); answer: the surface area of cuboid is 220 square centimeter, the volume is 200 cubic centimeter. The surface area of square is 6 × (6 × 6) = 6 × 36 = 216 (square centimeter); the volume of cube is 6 × 6 = 36 × 6 = 216 (cubic centimeter) ）A: the surface area of a cube is 216 square centimeters and its volume is 216 cubic centimeters

The larger the surface area is, the larger the volume is

Not necessarily. Surface area and volume are two different concepts
Surface area is the sum of all the surfaces of an object, and volume is the space occupied by the object
For example, if a small cylinder is dug out in the middle of a cylinder to become a circular tube, its surface area will be greatly increased and its volume will be reduced compared with the original cylinder

For a solid figure, () is called its surface area; () is called its volume?

The total area of all the faces of a solid figure is called its surface area
The space occupied by a solid figure is called its volume

In the triangular pyramid a-bcd, the side edges AB, AC and AD are perpendicular. If the areas of △ ABC, △ ACD and △ ADB are √ 2 / 2, √ 3 / 2 and √ 5 / 2 respectively, what is the volume of the triangular pyramid?