# Solid geometry, stereometry - page 15

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. 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%?
2. 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?
3. 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.
4. Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
5. Circular pool
The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
6. Big cube
Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.
7. 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.
8. How much
How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
9. 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?
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. 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.
12. Cube edges
The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
13. Rainfall
A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
14. 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.
15. Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
16. Basen
How many square meters of tiles we need to tile the walls and floor of the pool 15 meters long, six meters wide and two meters?deep
17. Rain
It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
18. Inscribed
Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
19. Container
The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
20. Seawater
Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.

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