# Cube + volume - math problems

1. Magnified cube If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
2. Cone from cube The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3
3. Kostka Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
4. 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.
5. The largest The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
6. The edge of a cube How much does the edge of a cube of 54.9 cm3 measure?
7. Surface of the cube Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
8. Water container The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
9. Nádoba Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby?
10. A plasticine Jožko modeled from plasticine. He used 27g of plasticine to model a 3 cm long cube. How many grams of plasticine will it need to mold cubes with an edge of 6cm?
11. Length of the edge Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
12. Cube construction A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
13. Space diagonal The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
14. 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?
15. The cube The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?
16. Cube surface and volume The surface of the cube is 500 cm2, how much cm3 will be its volume?
17. The number The number of 1 cm cubes required to make 4 cm cube is?
18. Calculate 3 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
19. Cube cut In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
20. The volume 2 The volume of a cube is 27 cubic meters. Find the height of the cube.

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