# 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. Barrel with water
The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
2. 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?
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. 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.
5. Cube walls
Find the volume and the surface area of the cube if the area of one of its walls is 40 cm2.
6. Hectoliters
How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
7. Tropical, mild and arctic
How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.
8. No smoke
Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a gian
9. Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
10. Hemispherical hollow
The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
11. Cube edges
The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
12. An oil
An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
13. 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.
14. The diagram
The diagram is a cone of radius 8cm and height 10cm. The diameter of the base is. ..
15. Cylinder melted into cuboid
A circular cylinder has area of cross section 56cm2 and the height is 10cm the cylinder is melted and made into a cuboid of base area 16cm2. What is the height of the cuboid?
16. Stones in aquarium
In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
17. If one
If one litre of pant covers an area of 5 m2 how much paint is needed to cover: a) rectangular swimming pool With dimensions 4m x 3m x 2.5m (the Inside walls and the floor only) b) the Inside walls and floor of a cylindrical reservoir with diameter 3m an
18. Big cube
Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.
19. The volume
The volume of a solid cylinder is 260 cm3 the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
20. 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?

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