# 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. Cube edges If the edge length of the cube increases by 50%, how does the volume of this cube increase?
2. Rainfall A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
3. Iron ball The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
4. Inscribed Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
5. Prism 4 sides Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
6. Basen How many square meters of tiles we need to tile the walls and floor of the pool 15 meters long, six meters wide and two meters?deep
7. Container The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
8. Rain It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
9. Rectangular prism If i have a rectangular prism with a length of 1,000 cm, width of 30 cm and a height of 50 cm, what is the volume?
10. Tropical, mild and arctic How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.
11. Cube The sum of all cube edges is 30cm. Find the surface area of the cube.
12. Seawater Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
13. Edges or sides Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
14. Cylinder-shaped vase If the cylinder-shaped vase is filled with water up to 35 cm, it contains 1 liter of water. How much water will it contain if it is filled to a height of 45cm?
15. Aquarium Can 30 liters of water fit in a cuboid aquarium with dimensions a = 3dm b = 6dm c = 5dm?
16. Hemispherical hollow The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
17. Spherical tank The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
18. Hectoliters How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
19. If one If one litre of pant covers an area of 5 m2 how much paint is needed to cover: a) rectangular swimming pool With dimensions 4m x 3m x 2.5m (the Inside walls and the floor only) b) the Inside walls and floor of a cylindrical reservoir with diameter 3m and
20. Barrel with water The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...