# 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. Cuboid 5 Calculate the mass of the cuboid with dimensions of 12 cm; 0.8 dm and 100 mm made from spruce wood (density = 550 kg/m3).
2. Aquarium II Calculate how much glass we need to build an aquarium with a rectangular shape with base 70 cm × 70 cm and a height of 70 cm, if the waste is 2%. Aquarium haven't top glass.
3. Iron fence One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
4. Granite cube What is the weight in kg granite cube with an edge of 0.5 m if 1dm3 of granite weight 2600 g?
5. Surface of the cylinder Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
6. Copper plate Copper plate length 3.2 m and width 50 cm weighs 55.42 kg. What is the plate thick, if 1 m3 of copper weighs about 8700 kg?
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 and water How many liters of water can fit into a cube with an edge length of 0.11 m?
9. Cube 6 Volume of the cube is 216 cm3, calculate its surface area.
10. Cone and cube About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r?
11. Water On the lawn which has area 914 m2 rained 3 mm of water. How many liters of water rained?
12. 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?
13. Cubes Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
14. Observatory Observatory dome has the shape of a hemisphere with a diameter d = 10 m. Calculate the surface.
15. Gasholder The gasholder has spherical shape with a diameter 20 m. How many m3 can hold in?
16. Swimming pool 4 The pool shaped cuboid measuring 12.5 m × 640 cm at the bottom is 960hl water. To what height in meters reaches the water level?
17. Lathe Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
18. Pool coating How many pieces of tiles 25 cm × 15 cm need to coat the bottom and side walls of the pool with bottom dimensions 30 m × 5 m, if the pool can fit up to 271500 liters of water?
19. Bricks Openings in perforated bricks occupy 10% and brick has dimensions 30 cm, 15 cm and 7.5 cm. Calculate a) the weight of a perforated bricks, if you know that the density of the full brick material is p = 1800 kg/m3 (1.8 kg/dm3) b) the number of perforated.
20. Water tank 2 Water tank cuboid is 12 meters long and 6.5 meters wide and 1.2 meters high. How many hectoliters are in the tank when it is filled to 81%?

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