# 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. 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.
2. Milimeters The pool is 6 meters long, 3 meters wide and the water in it is filled with water to a height 1.7 m. When John jumped into it and completely submerged, the level has risen by 5.4 mm. How much weight John when we know that one liter of the human body weighs
3. Cube corners The wooden cube with edge 64 cm was cut in 3 corners of cube with edge 4 cm. How many cubes of edge 4 cm can be even cut?
4. Brass tube The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
5. Aluminum wire Aluminum wire of 3 mm diameter has a total weight of 1909 kg and a density of 2700 kg/m3. How long is the wire bundle?
6. Sphere fall How many percent fall volume of sphere if diameter fall 10×?
7. Cylinder - h2 Cylinder volume is 2.6 liters. Base area is 1.3 dm2. Calculate the height of the cylinder.
8. Conserving water Calculate how many euros are spent annually on unnecessary domestic hot water, which cools during the night in pipeline. Residential house has 129 m of hot water pipelines 5/8" and the hot water has a price of 7 Eur/m3.
9. Scale Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality?
10. Tin with oil Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
11. Special cube Calculate the edge of cube, if its surface and its volume is numerically equal number.
12. Eight blocks Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
13. Sphere area A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
14. Pot Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
15. Cubes Most how many cubes with an edge length of 5 cm may fit in the cube with the inner edge of 0.4 m?
16. Cuboid aquarium Cuboid 25 times 30 cm. How long is third side if cuboid contains 30 liters of water?
17. Aquarium 6 How high is the water level in the aquarium with a rectangular base 40cm and 50cm if it is filled 0,65hl of water?
18. Truncated cone Calculate the volume of a truncated cone with base radiuses r1=13 cm, r2 = 10 cm and height v = 8 cm.
19. Solid in water The solid weighs in air 11.8 g and in water 10 g. Calculate the density of the solid.
20. Cylinder The cylinder surface is 922 dm2, its height is equal to the radius of the base. Calculate height of this cylinder.

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