Solid geometry, stereometrySolid 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 dm2 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 cm3. 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 dm3.
- 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 m2 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 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
- 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 . .. )?
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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