# Third power + body volume - math problems - page 2

1. Cube and water How many liters of water can fit into a cube with an edge length of 0.11 m?
2. Lathe Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
3. Sphere fall How many percent fall volume of sphere if diameter fall 10×?
4. 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?
5. 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?
6. Tetrahedral prism The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm3.
7. Cube basics How long is the edge length of a cube with volume 23 m3?
8. Cube 7 Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
9. 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
10. 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.
11. Cube containers Two containers shaped of cube with edges of 0.7 m and 0.9 m replace a single cube so that it has the same volume as the original two together. What is the length of the edges of the new cube?
12. Prism bases Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
13. Cube-shaped box Design the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, 6cm small cubes could be stacked to make full use of the box space (each type of cube separately). Can you find out how many smallest cubes are in the box?
14. Cube One cube has edge increased 5 times. How many times will larger its surface area and volume?
15. Cuboid edges in ratio Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
16. Volume and area What is the volume of a cube which has area of 361 cm2?
17. Volume and body diagonal Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
18. Minimum surface Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
19. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
20. Cube edges If the edge length of the cube increases by 50%, how does the volume of this cube increase?

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...