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. Bottle
A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
2. Perfect cubes
Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube?
3. Volume of ball
Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
4. A cylindrical tank
A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
5. The volume 2
The volume of a cube is 27 cubic meters. Find the height of the cube.
6. Area to volume
If the surface area of a cube is 486, find its volume.
7. Cube
The sum of all cube edges is 30cm. Find the surface area of the cube.
8. 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.
9. Orlík hydroelectric plant
The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the
10. Bucket
The bucket half filled with water weighs 5.55 kg, the full bucket weighs 9.85 kg. How much does the bucket weigh?
11. Cube surface and volume
Find the surface of the cube with a volume of 27 dm3.
12. 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?
13. 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?
14. Dort
The cube-shaped cube box has the dimensions of 30 cm × 30 cm × 12 cm. How many CZK (Czech crowns) would cost be the biggest cake that would fit into the box when a 10 cm³ cake costs CZK 0.5? The cake has the same shape as the box.
15. The cube
The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
16. Cage
How many m2 of mesh farmer use for fencing of a cuboid cage with dimensions 25m, 18m, and 2.5m?
17. Spherical tank
The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
18. Children's pool
Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m2 of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool?
19. Edges or sides
Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
20. Seawater
Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.

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