# 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. Water In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water?
2. Cuboid - simple Calculate the surface area and volume of a cuboid if a = 8 cm, b = 14 cm and c = 6 cm.
3. Wood planks 1 m3 of wood planks costs 179 EUR. How much will I pay for 11 planks measuring 6 cm, 10 cm and 6 m?
4. Concrete pillar How many m³ of concrete is needed for the construction of the pillar shape of a regular tetrahedral prism, when a = 60 cm and the height of the pillar is 2 meters?
5. Cube 3 How many times will increase the volume of a cube if we double the length of its edge?
6. Cube 2 How many times will increase if the surface area of the cube if we triple length of its edge?
7. Cuboids in cube How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
8. Cube How many times increases the surface area of a cube with edge 23.4 cm if the length of the edge doubled?
9. Stone When Peter threw stone in a box of water he discovered that the water level has risen by 6 cm. The box has a cuboid shape, the bottom has dimensions of 24 cm and 14 cm, height is 40 cm. What volume has a stone?
10. Water pool What water level is in the pool shaped cuboid with bottom dimensions of 25 m and 10 meters, when is 3750hl water in the pool.
11. Snow Snow fell overnight layer of thickness 19 cm. In the morning I had to clear a path 69 m long and one meter wide. How many cubic meters of snow I clear? How many kilos was it? (1 m3 fresh snow weighs 350 kg)
12. Concrete box The concrete box with walls thick 5 cm has the following external dimensions: length 1.4 m, width 38 cm and height 42 cm. How many liters of soil can fit if I fill it to the brim?
13. Soil pit Workers dug a pit cube with edge 2.5 meters. How many cars shall remove soil if the car suddenly take 4m³ of soil?
14. Painter How many euros we will pay for repainting the room shaped cuboid with a length of 4.5 meters, width of 2.5 meters and a height of 3 meters, if for 1 m2 with paint we pay € 1.5?
15. Milimeters The pool is 6 meters long, 3 meters wide and the water in it is filled with water to a height 1.7 m. When John jumped into it and completely submerged, the level has risen by 5.4 mm. How much weight John when we know that one liter of the human body weigh
16. Water lake The length of the lake water is 8 meters width 7 meters and depth 120 centimeters. How many liters of water can fit into the water lake?
17. Cubes - diff Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
18. Two boxes-cubes Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
19. Brass tube The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
20. Sphere area A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.

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