# 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. The coil How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
2. Annual rainfall The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
3. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
4. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
5. Body diagonal Calculate the length of the body diagonal of the 6cm cube.
6. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
7. Cone 15 The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
8. Cuboidal room Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
9. Tetrahedron What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
10. Regular triangular pyramid Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
11. Butter At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain? The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
13. 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
14. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
15. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
16. Regular prism The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
17. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
18. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
19. Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
20. 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.

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