# Volume + cube root - problems

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. Cube in a sphere The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
3. Transforming cuboid Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
4. Cone Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
5. Cylinder Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.
6. Lead cube Calculate the edge of the cube made ​​from lead, which weighs 19 kg. The density of lead is 11341 kg/m3.
7. 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
8. Shots 5500 lead shots with diameter 4 mm is decanted into a ball. What is it diameter?
9. Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
10. Iron sphere Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
11. 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.
12. Chemical parison The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
13. 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.
14. Cube 6 Volume of the cube is 216 cm3, calculate its surface area.
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. 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
19. 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.
20. Cube 9 What was the original edge length of the cube if after cutting 39 small cubes with an edge length 2 dm left 200 dm3?

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