# Third power + body volume - math problems

- Cuboid and ratio

Find the dimensions of a cuboid having a volume of 810 cm^{3}if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5 - Wall thickness

The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm^{3}. - The ball

The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger? - Length of the edge

Find the length of the edge of a cube that has a cm^{2}surface and a volume in cm^{3}expressed by the same number. - Alien ship

The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. - 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? - Calculate 3

Calculate the cube volume whose edge is 3x-1,3x-1,3x-1 - Volume of ball

Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π - The volume 2

The volume of a cube is 27 cubic meters. Find the height of the cube. - Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm^{3}. - Body diagonal

Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal. - Edges or sides

Calculate the cube volume, if the sum of the lengths of all sides is 276 cm. - Seawater

Seawater has a density of 1025 kg/m^{3}, ice 920 kg/m^{3}. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge. - 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. - 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 cm^{2}. Find the area of the - No smoke

Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant - Cube edges

If the edge length of the cube increases by 50%, how does the volume of this cube increase? - 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%? - 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 cm^{3}.

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