# 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. Iron ball The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
2. Half-sphere roof The roof above the castle tower has the shape of a 12.8 m diameter half-sphere. What is the cost of this roof, if the cost of 1 square meter is 12 euros and 40 cents?
3. The number The number of 1 cm cubes required to make 4 cm cube is?
4. Aquarium Can 30 liters of water fit in a cuboid aquarium with dimensions a = 3dm b = 6dm c = 5dm?
5. Calculate 3 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
6. Bottle A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
7. TV transmitter The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
8. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
9. Pool The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
10. Transforming cuboid Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
11. Sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
12. Eiffel Tower Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?
13. Pipes Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
14. Tanks Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
15. Gutter How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
16. Barrel of oil Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel?
17. Bricks Brick has volume 2.2 dm3. How many bricks can drive truck with capacity 23 ton? The density of brick is 1.6 g/cm3.
18. Cube zoom How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
19. Sand pile Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c
20. Lathe From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?

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