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.

Correct result:

x =  12 cm
y =  10 cm
z =  10 cm


n=50 a=4 cm b=3 cm c=2 cm  V=n a b c=50 4 3 2=1200 cm3 1200=2×2×2×2×3×5×5=24×3×52  S=2 (xy+yz+xz)min  x1=V3=1200310.6266 cm  x=2 2 3=12 cm
y=5 2=10 cm
z=V/(x y)=1200/(12 10)=10 cm

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

Showing 0 comments:

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

  • Prism X
    Cuboid_simple The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
  • Area of a cube
    kocky_2 Calculate the surface area of a cube if its volume is equal to 729 cubic meters.
  • Diameter = height
    valec_1 The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
  • Volume and area
    cubes_8 What is the volume of a cube which has area of 361 cm2?
  • Cube-shaped box
    cubes2 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?
  • Two rectangular boxes
    cuboid_2 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.
  • Equilateral cylinder
    3d Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
  • The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  • Prism bases
    hranoly 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.
  • Cuboid
    dodecagon The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?
  • Length of the edge
    cube_shield Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
  • Iron sphere
    sphere_1 Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
  • Cuboid and ratio
    cuboid_2 Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
  • Surface of cubes
    cubes3_6 Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
  • Cremons
    wagon The freight wagon is shaped like cuboid 21m and 3.5m and 4.2m How many cremons can be loaded if one is a cube with an edge length of 7 cm?
  • Two boxes-cubes
    3-kostky 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?
  • Cube surface and volume
    cube_shield_6 Find the surface of the cube with a volume of 27 dm3.