# 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. Cone area and side Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
2. Cork and swimming If a person weighs 80 kg, how many kilograms of cork must take swimming belt to use it to float on water? The density of the human body is 1050kg/m3 and cork 300kg/m3. (Instructions: Let the human body and cork on a mixture that has a density of 1000kg/m
3. Wood planks 1 m3 of wood planks costs 179 EUR. How much will I pay for 11 planks measuring 6 cm, 10 cm and 6 m?
4. Ice and water We want to cover rectangular rink with dimensions of 55 m and 25 m with 4cm thick layer of ice. How many liters of water we need if after freezing water increases its volume by 10%?
5. Cube 8 The surface of the cube is 0.54 m2. Calculate the length of the cube edge.
6. Cuboid - edges The sum of all edges cuboid are 8 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid.
7. Fe vs. H2O The volume of what the body of the same weight is greater - iron or water?
8. Copper wire What is the weight of 1000 m copper wire with a diameter of 5 mm when rezistivity p = 8.8 g / cm3?
9. Cuboid box How many m2 paper is needed for the sticking cuboid box of dimensions 50 cm, 40 cm and 30 cm? To the folds add one-tenth the area.
10. Glass door What is the weight of glass door panel 5 mm thick height 2.1 meters and a width of 65 cm and 1 cubic dm of glass weighs 2.5 kg?
11. Water lake The length of the lake water is 8 meters width 7 meters and depth 120 centimeters. How many liters of water can fit into the water lake?
12. Wood cuboid What is the weight of the wood cuboid 15 cm, 20 cm, 3 m if 1 m3 wood weighs 800 kg?
13. Spheres in sphere How many spheres with a radius of 15 cm can fits into the larger sphere with a radius of 150 cm?
14. Cardboard How many m2 of cardboard are needed to make the cuboid with dimensions 40 cm 60 cm and 20 cm?
15. Digging A pit is dug in the shape of a cuboid with dimensions 10mX8mX3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m X 30m. What is the increase in the level of the plot ?
16. Freezer The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, 30 cm. A layer of ice of 23 mm thick was formed on the inner walls (and on the opening) of the freezer. How many liters of water will drain if we dispose the freezer?
17. Gasoline tank cylindrical What is the inner diameter of the tank, which is 8 m long and contains 40 cubic cubic meters of gasoline?
18. Cube-shaped box Design the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, 6cm small cubes could be stacked to make full use of the box space (each type of cube separately). Can you find out how many smallest cubes are in the box?
19. Aquarium Aquarium is cube with edge 45 cm. How much water can fit in there?
20. Container The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?

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