# 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. Lathe From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
2. Rotation The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
3. Air mass What is the weight of the air in a classroom with dimensions 10 m × 10 m × 2.7 m ? The air density is 1.293 kg/m3.
4. Cube Calculate the surface cube with edge 11 dm.
5. Prism X The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
6. Hollow sphere Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm3), if the inner diameter is 14 cm and wall thickness is 3 mm.
7. Cone Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
8. Cube The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
9. Balls Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
10. Cube in ball Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
11. Hole In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
12. Air Room is 35.6 m long, 19.6 dm wide and 591 cm high. How many people can simultaneously be in this room if for hygiene reasons is calculated 5000 dm3 of air per person?
13. Copper sheet The copper plate has a length of 1 m, width 94 cm and weighs 9 kg. What is the plate thickness, if 1 m3 weighs 8715 kg?
14. Cubes Cube, which consists of 27 small cubes with edge 4 dm has volume:
15. Tetrapack How high should be the milk box in the shape of a prism with base dimensions 8 cm and 8.8 cm if its volume is 1 liter?
16. Water Into a full cylindrical tank high 3.6 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.9 m, 0.7 m. How many liters of water will come out?
17. 2x cone Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
18. Hole They fill shape hole with dimensions 2.9 m, 17 m, 15.2 m with 97 m3 of soil. How many percent it fill up?
19. Aquarium Aquarium is rectangular box with square base containing 76 liters of water. Length of base edge is 42 cm. To what height the water level goes?
20. Balls Ping pong balls have a diameter of approximately 5.1 cm. They are sold in boxes of 10 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled.

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