# 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. Prism Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
2. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
3. Wood lumber Wooden lumber is 4 m long and has a cross section square with side 15 cm. Calculate: a) the volume of lumber b) the weight of the lumber if 1 m3 weighs 790 kg
4. Cuboid and eq2 Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm2.
5. Body diagonal The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
6. Cube and sphere Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
7. Square vs rectangle Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
8. Rectangle pool Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
9. Glass aquarium How many m2 of glass are needed to produce aquarium with bottom dimensions of 70 cm x 40 cm and 50 cm high?
10. Cuboid easy The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
11. Chocolate roll The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
12. Octahedron - sum On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also
13. MO SK/CZ Z9–I–3 John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
14. Moon We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
15. Wall diagonal Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
16. Content area and percents Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%.
17. Average speed What is the average speed you have to move the way around the world in 80 days? (Path along the equator, round to km/h).
18. Glass How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
19. Cube 5 The content area of one cube wall is 32 square centimeters. Determine the length of its edges, its surface and volume.
20. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.

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