# 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. Painter How many euros we will pay for repainting the room shaped cuboid with a length of 4.5 meters, width of 2.5 meters and a height of 3 meters, if for 1 m2 with paint we pay € 1.5?
2. Water tank The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
3. Concrete pipe How much will cost cover a 6 m long concrete pipe with an outer radius 1.5 m and inner radius 0.8 meters if 1 m2 paint costs 24 €.
4. The factory The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3?
5. Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
6. Cylinder diameter The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?
7. Cuboid and ratio Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
8. Cylinder twice If the radius of the cylinder increases twice, and the height is reduced twice, then the volume of the cylinder increases (how many times?):
9. Hollow sphere The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
10. Mass The thickness of a metallic tube is 1cm and its outer radius is 11cm. Find the mass of such 1m long tube, if the density of the metal is 7.5g per cubic cm.
11. Cuboid - ratios The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm2. Calculate the surface area and volume of this cuboid.
12. CuZn Brass is an alloy of copper and zinc. The 10 centimeter brass cube has a weight of 8.6 kg. Copper density is 8930 kg/m3, the zinc density is 7130 kg/m3. Calculate how many kg of copper and zinc a cube contains.
13. Cube 2 How many times will increase if the surface area of the cube if we triple length of its edge?
14. Fuel economy How many kilometers is sufficient petrol in the cylinder fuel tank with a diameter 40 cm and the base of tank length 1 m, when it is filled to 60% and if the car consume 15 liters per 100 km?
15. Cube surface area The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased.
16. Tank To cuboid tank whose bottom has dimensions of 9 m and 15 m were flow 1080 hectoliters of water. This was filled 40% of the tank volume. Calculate the depth of the tank.
17. Cylinder surface area Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm3. Calculate its surface area.
18. Cube How many times increases the surface area of a cube with edge 23.4 cm if the length of the edge doubled?
19. Cube edge Determine the edges of the cube when the surface is equal to 37.5 cm square.
20. Pool The pool has the shape of a cylinder with a diameter 4.6m, the presumed height is 130cm. The bucket fits 12l of water. How many buckets do you have to bring to fill this pool?

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