# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

1. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
2. Sphere VS Find the surface and volume of a sphere that has a radius of 2 dm. The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
4. Winch The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
5. Sphere floating Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
6. Castle model The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm2 of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of wo
7. Gravitation From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
8. Water tank What is the height of the cuboid-shaped tank with the bottom dimensions of 80 cm and 50 cm if the 480 liters of water reaches 10 cm below the top?
9. Centroid - two bodies A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
10. Prism 4 sides Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
11. 3rd dimension The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
12. The cube The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?
13. Cube root For 13, Sam wrote 2891 instead of the correct cube number. By how much was he wrong?
14. Iron ball The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
15. Half-sphere roof The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is the cost of this roof, if the cost of 1 square meter is 12 euros and 40 cents?
16. Cube surface and volume The surface of the cube is 500 cm2, how much cm3 will be its volume?
17. The number The number of 1 cm cubes required to make 4 cm cube is?
18. The observatory The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal needs to be covered to cover it, and 15 percent must be added to the minimum amount due to joints and waste?
19. Aquarium Can 30 liters of water fit in a cuboid aquarium with dimensions a = 3dm b = 6dm c = 5dm?
20. Calculate 3 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1

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