# 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. Water well
Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
2. Concrete pipe
How much will cost cover a 6 m long concrete pipe with an outer radius 1.5 m and inner radius 0.8 meters if 1 m2 paint costs 24 €.
3. Volume from surface area
What is the volume of the cube whose surface area is 96 cm2?
4. Tray
Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
5. For thinkings
The glass cube dive into the aquarium, which has a length of 25 cm, width 20 cm and height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge?
6. Rotary cylinder 2
Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm3?
7. Concrete tank
How many m3 of concrete is in the tank shape of a cuboid with dimensions of 2000 cm and 5.6 meters and 70 dm, if the concrete takes up 3/7 of the tank?
8. Hollow sphere
Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
9. Swimming pool 4
The pool shaped cuboid measuring 12.5 m × 640 cm at the bottom is 960hl water. To what height in meters reaches the water level?
10. Pot
Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
11. Liters od milk
The cylinder-shaped container contains 80 liters of milk. Milk level is 45 cm. How much milk will in the container, if level raise to height 72 cm?
12. Surface area
The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
13. Water level
The glass container has a cuboid shape with dimensions of the bottom 24 cm and 12 cm. The height of water is 26 cm. Calculate the volume of the body, which are sunk into the water if the water level rise by 3 cm.
14. Earth's surface
The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?
15. Cube basics
How long is the edge length of a cube with volume 15 m3?
16. Cuboid
Find the cuboid that has the same surface area as the volume.
17. Iron fence
One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
18. Chemical parison
The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
19. Milk package
Milk is sold in a box with dimensions of 9.5 cm; 16.5 cm and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible.
20. Cylinder - area
The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.

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