# 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. Weight of air What is the weight of air in the living room measuring width 5 m length 2 m and height 2.8 m? Air density is ρ = 1.2 kg/m3.
2. Shots 5500 lead shots with diameter 4 mm is decanted into a ball. What is it diameter?
3. Water container Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container?
4. Sphere growth How many times grow volume of sphere if diameter rises 10×?
5. Cone in cylinder The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage.
6. Icerink Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water.
7. Iron sphere Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
8. Snow Snow fell overnight layer of thickness 19 cm. In the morning I had to clear a path 69 m long and one meter wide. How many cubic meters of snow I clear? How many kilos was it? (1 m3 fresh snow weighs 350 kg)
9. 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.
10. Volume from surface area What is the volume of the cube whose surface area is 96 cm2?
11. Cubes Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
12. Cone If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
13. Chemical parison The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
14. Cuboid The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?
15. Liters in cylinder Determine the height at which level 24 liters of water in a cylindrical container having a bottom diameter 36 cm.
16. Ice cream in cone In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
17. Stones in aquarium In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
18. Volume and surface Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
19. Carpenter From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
20. Cone in cube The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage.

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