# 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.

- Lathe

From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed? - 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. - 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/m^{3}. - Cube

Calculate the surface cube with edge 11 dm. - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm^{3}. What is the area of surface of the prism? - Hollow sphere

Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm^{3}), if the inner diameter is 14 cm and wall thickness is 3 mm. - 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. - Cube

The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller? - Balls

Three metal balls with volumes V_{1}=71 cm^{3}V_{2}=78 cm^{3}and V_{3}=64 cm^{3}melted into one ball. Determine it's surface area. - 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? - 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? - 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 dm^{3}of air per person? - 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 m^{3}weighs 8715 kg? - Cubes

Cube, which consists of 27 small cubes with edge 4 dm has volume: - 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? - 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? - 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. - Hole

They fill shape hole with dimensions 2.9 m, 17 m, 15.2 m with 97 m^{3}of soil. How many percent it fill up? - 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? - 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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