# 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. Equilateral cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
2. Cube, cuboid, and sphere Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
3. Cuboid - Vab Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters.
4. Volume and body diagonal Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
5. Cube into sphere The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
6. The tank The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?
7. Minimum surface Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
8. 3rd dimension The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
9. Circular pool The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
10. Cylindrical container An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
11. Cube surface and volume Find the surface of the cube with a volume of 27 dm3.
12. How much How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
13. Big cube Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.
14. Cuboid walls If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
15. Children's pool Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m2 of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool?
16. Orlík hydroelectric plant The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the p
17. Water tank A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
18. Living room How many people can live in a room with dimensions: a = 4m b = 5m c = 2.5m if one person needs 15m cubic space (i. E. Air . .. )?
19. Cuboid The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
20. Cube edges The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.

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