# Volume + length - math problems

1. The copper wire The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
2. Two rectangular boxes Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface. The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
4. Cylinder The 1.8m cylinder contains 2000 liters of water. What area (in dm2) of this container is the water?
5. Tetrahedral pyramid A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
6. Space diagonal The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
7. A sculptor A sculptor is duplicating a statue based on an original statue. If the scale factor of the replication is 3.2, will the new statue be larger or smaller than the original statue (enter 1 = larger, 0= smaller)
8. 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?
9. 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?
10. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
12. Iron density Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
13. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
14. Water level How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
15. Density of the concrete Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
16. Container The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
17. 3d printer 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
18. Hectoliters How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
19. Sand path How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
20. 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.

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