# 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 2 Empty barrel weighs 7 kg. When it filled with water up to 45% height, weighs 60 kg. How heavy is barrel full of water?
2. Cross-sections of a cone Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
3. Water in aquarium The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water.
4. Swimming pool The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
5. Cube corners From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
6. Pool 3 How long will fill pool cuboid shape (8m 6m 1.5m) when flows 15 liters/s?
7. Water In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water?
8. Flowerbed The flowerbed has a length 3500mm and a width 1400mm. How many foil is needed to covers the flowerbed? How many m2 of foil was consumed for its production (add 10% of the material to the joint and waste)? How many liters of air is inside the enclosure? (F
9. Fire tank How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?
10. Cuboid walls Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
11. Cuboid How many times will increase the volume of a cuboid, if one dimension is twice larger, second dimension three times larger and third dimension four times lower?
12. Cylinder The cylinder-shaped container has 80 liters of water. The water reaches 45 cm height. How many liters of water will be in a container if water level extend to a height 72 cm? Write the result in liters, write down only as a whole or decimal number.
13. Truck of milk How many hectoliters of ,,the box" milk fit in the truck, ake cargo size area is 2.8 m x 3 m x 17 m? A liter of milk in a box measuring 12 cm x 7 cm x 20 cm.
14. Concrete pillar How many m³ of concrete is needed for the construction of the pillar shape of a regular tetrahedral prism, when a = 60 cm and the height of the pillar is 2 meters?
15. Cube 7 Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
16. Cuboid - complicatef Three walls of the same cuboid has content 6 cm2, 10 cm2 and 15 cm2. Calculate the volume of the cuboid.
17. Ring The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
18. Cube 3 How many times will increase the volume of a cube if we double the length of its edge?
19. Sportsman A trained athlete is able to exhale after a deep breath still 500 ml of air. At normal inhalation and exhalation is breathing 500 ml of air. Within one minute, one breath and exhaled 14 times. What part of breathing air per day is one exhalation?
20. Metal box How much metal we need for the production of box with dimensions 5 dm, 30 cm and a height of 1 m? Add 12% of the waste and folds.

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