# 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. An oil An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
2. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
3. Winch The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
4. Hectoliters How deep is the pool if there are 2025 hectoliters of water and the bottom dimensions are a = 15 meters b = 7,5 meters and the water level is up to 9/10 (nine-tenths) of height. Alaska is the largest state in the United States and has a surface area of approximately 588,000 square miles. Montana has a surface area that is approximately 25% of the surface area of Alaska. What is the approximate surface area of Montana?
6. The volume 2 The volume of a cube is 27 cubic meters. Find the height of the cube.
7. Cylindrical tank 2 If a cylindrical tank with volume is used 12320cm raised to the power of 3 and base 28cm is used to store water. How many liters of water can it hold?
8. Calculate 3 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
9. The diagram The diagram is a cone of radius 8cm and height 10cm. The diameter of the base is. ..
10. Cage How many m2 of mesh farmer use for fencing of a cuboid cage with dimensions 25m, 18m, and 2.5m?
11. Reservoir 3 How many cubic feet of water is stored in the reservoir that has a length of 200 feet, a width of 100 feet, an overflow depth of 32 feet, and a current water level of 24 feet?
12. Cube root For 13, Sam wrote 2891 instead of the correct cube number. By how much was he wrong?
13. Aquarium I have an aquarium that is 100 cm long and 40 cm wide and 40 cm in height. We fill it with water. How much will it weigh?
14. Wood prisms How many weight 25 prisms with dimensions 8x8x200 cm? 1 cubic meter of wood weighs 800 kg.
15. Rainwater The garden area of 800 square meters fell 3mm of rainwater. How many 10 liters of water can we water this garden equally?
16. Pebble The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
17. Diameter of a cylinder I need to calculate the cylinder volume with a height of 50 cm and a diameter of 30 cm.
18. Heptagonal pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 0.10 grams/cm3.
19. The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
20. A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.

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