# 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. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
2. Cubes
Cube, which consists of 27 small cubes with edge 4 dm has volume:
3. 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?
4. Pool
The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
5. Cubes
Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
6. 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.
7. Cube
The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
8. Water
Into a full cylindrical tank high 3 with base radius 2.4 m we insert cuboid with dimensions 1.7 m, 1.7 m, 0.8 m. How many liters of water will come out?
9. Cube corners
The wooden cube with edge 64 cm was cut in 3 corners of cube with edge 4 cm. How many cubes of edge 4 cm can be even cut?
10. Cube corners
From cube of edge 5 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
11. Sea on the Moon
Assume that the Moon has sea, the same composition as on the Earth (has same density of salt water). Calculate dive of boat floating in the sea on the Moon, when on Earth has dive 3.6 m. Consider that the Moon has 6.5-times smaller gravitational accelerat
12. Pipe
How long is the pipe with an outside diameter of 1.44 m if his coloring consumed 44 kg of color. 1 kg of color coverage is 9 m2.
13. Cube
Calculate the surface cube with edge 11 dm.
14. 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?
15. Shots
5500 lead shots with diameter 4 mm is decanted into a ball. What is it diameter?
16. Sphere
The surface of the sphere is 12100 cm2, and the weight is 136 kg. What is its density?
17. Cube
The sum of lengths of cube edges is 57 cm. What is its surface and volume?
18. Special cube
Calculate the edge of cube, if its surface and its volume is numerically equal number.
19. Rotating cone
Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm.
20. Observatory
Observatory dome has the shape of a hemisphere with a diameter d = 16 m. Calculate the surface.

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