1. After sawing a cuboid 5 cm, the remaining part is just a cube, and the surface area is reduced by 40 square cm. What is the volume of the original cuboid? 2. In a gymnastic room, 1800 pieces of wood floor with a length of 40 cm, a width of 15 cm and a thickness of 4 cm are laid. How large is the gymnastic room? 3. Use two cubes of the same size to make a cuboid. If the total edge length of the cubes is 96cm, what is the volume of the cuboid and the surface area of the original cube?

Question 1: the side length of a square is (40 / 4) / 5 = 2
The side length of the cuboid is 2 + 5 = 7
So the cuboid volume is: 2 * 2 * 7 = 28
Question 2: Area s = 1800 * 40 * 15 = 1080000 square centimeters = 108 square meters
The total length of rectangle is equal to the sum of six sides
The side of the square is: 96 / 6 = 16
The cuboid volume v = 16 * 16 * 32 = 8192
The surface area of the cube is s = 10 * 16 * 16 = 2560

Three mathematical geometry problems
1. In the triangle ABC, the angle ACB is 90 degrees, the angle B is 60 degrees, CD is perpendicular to AB and D
2. Known: in the triangle ABC, ab = AC, angle B = 75 degrees, CD is perpendicular to AB and D, prove: CD = half ab
3. In the triangle ABC, the angle BAC = 90 degrees, ad perpendicular to BC and D, de perpendicular to AC and E, the angle DAC = 30 degrees, CE = 2, find the length of BC
In a right triangle, if an acute angle is equal to 30 degrees, the right side it faces is half of the hypotenuse
There are also Pythagorean theorem, inverse theorem of Pythagorean theorem and so on

1. Prove: in triangle ABC, because angle ACB = 90 degrees, angle B = 60 degrees, so angle a = 30 degrees, so AB = 2BC. In triangle BCD, because CD is perpendicular to AB and D, so angle BDC = 90 degrees, because angle B = 60 degrees, so angle BCD = 30 degrees, so BC = 2bd, so AB = 4bd, and ab = AD + BD, so ad = 3bd

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