# 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.

- 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. - 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? - 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. - 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%? - Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste. - 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? - 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. - 3rd dimension

The block has a surface of 42 dm^{2}and its dimensions are 3 dm and 2 dm. What is the third dimension? - Circular pool

The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool? - Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm^{3}. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Cube surface and volume

Find the surface of the cube with a volume of 27 dm^{3}. - How much

How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč? - Big cube

Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long. - 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. - Children's pool

Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m^{2}of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool? - 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 m^{3}/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 - 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. - 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 . .. )? - 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. - Cube edges

The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.

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