# 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. Steel tube The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.
2. Aquarium The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edg
3. Seat How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
4. Water depth How many square meters of the inside of the pool wet the water if the pool is 25 meters long and 10 meters wide and the water depth is 1.2 meters everywhere.
5. Ratio of volumes If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
6. Angle of two lines There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
7. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
8. Height of the room Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
9. Metal tube Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
10. Iceberg What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
11. Triangular prism Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm. Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
13. Pyramid height Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
14. Prism 4 sides The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
15. Cube into cylinder If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
16. Castle tower The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap.
17. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
18. Spherical cap 4 What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
19. Pile of sand A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
20. The pot The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.

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

We will send a solution to your e-mail address. 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...