# Volume + third power - examples

1. Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
2. Sphere
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
3. Hollow sphere
Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm3), if the inner diameter is 14 cm and wall thickness is 3 mm.
4. Cube
The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
5. Cube in ball
Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
6. Hollow sphere
Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
7. Cube
The sum of lengths of cube edges is 69 cm. What is its surface and volume?
8. Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
9. Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
10. Cylinder - area
The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
11. Surface of the cylinder
Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
12. Granite cube
What is the weight in kg granite cube with an edge of 0.5 m if 1dm3 of granite weight 2600 g?
13. Cube and water
How many liters of water can fit into a cube with an edge length of 0.11 m?
14. Cuboids in cube
How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
15. Two boxes-cubes
Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
16. For thinkings
The glass cube dive into the aquarium, which has a length of 25 cm, width 20 cm and height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge?
17. Cube basics
How long is the edge length of a cube with volume 23 m3?
18. Cube 7
Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
19. Tower model
Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
20. 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.

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