# 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 diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
2. Allan
Allan keeps tropical fish. His aquarium is 4 feet long, 1 foot wide, and 2 feet tall. Each fish needs at least 0.5ft³ of water. What is the maximum number of fish that he can keep in the aquarium? Please show your solution. Please
3. Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
4. Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
5. Cylinder height
Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
6. Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
7. The aquarium
The aquarium has a capacity of 18 liters. What is its height when the square bottom is 8 2/3 cm long?
8. Paper box
Calculate whether 11 dm² of paper is sufficient for gluing a box without a lid with bottom dimensions of 2 dm and 15 cm and 12 cm high. Write result as: 0 = No, 1 = Yes
9. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
10. Body diagonal
Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
11. Water level
How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
12. Perpendicular prism
Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs.
13. Height as diameter of base
The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
14. Collect rain water
The garden water tank has a cylindrical shape with a diameter of 80 cm and a height of 12 dm. How many liters of water will fit into the tank?
15. Pool
The prism-shaped pool is 2 m deep with a bottom of the isosceles trapezoid with base dimensions of 10 m and 18 m and arm legs 7 m long and 5.7 m long. During the spring cleaning, the bottom and walls of the pool must be painted. How many m2 of paint shoul
16. Density of the concrete
Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
17. Slant height
The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
18. Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
19. 3d printer
3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
20. Perimeter of base
The circumference of the base of the rotating cylinder is same as its height. What is the diameter and height of this cylinder with volume 1 liter?

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