Cuboid and ratio

Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.

Correct result:

V =  1500 dm3

Solution:

V=abc a:b:c=1:2:6 a=1k b=2k c=6k S=1000 S=2(ab+bc+ac) S=2(2k2+12k2+6k2)=40 k2 k=S/40=1000/40=5 a=k=5 b=2⋅ k=2⋅ 5=10 c=6⋅ k=6⋅ 5=30 V=a⋅ b⋅ c=5⋅ 10⋅ 30=1500 dm3

Try another example


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:
avatar




Tips to related online calculators
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Cuboid - ratio
    cuboid_3colors Find the volume of a block whose dimensions are in the ratio 2: 3: 4 and the surface is 117 dm2.
  • 3rd dimension
    kvader_2 The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
  • Prism
    hranol4sreg_1 Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?
  • Volume and surface
    image001(1) Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
  • The cube
    cube_shield_1 The cube has a surface area of 216 dm2. Calculate: a) the content of one wall, b) edge length, c) cube volume.
  • Cube walls
    krychle_6 Find the volume and surface area of the cube if the area of one wall is 40cm2.
  • Cylinder height
    cylinder_9 Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
  • Edge of prism
    hranol4b_1 The regular quadrilateral prism has a surface of 250 dm2, its shell has a content of 200 dm2. Calculate its leading edge.
  • Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  • Cuboid - ratios
    kvader11 The sizes of the edges of the cuboid are in the ratio 2: 3: 5. The smallest wall have area 54 cm2. Calculate the surface area and volume of this cuboid.
  • Tetrahedral prism - rhomboid base
    rhombus2_2 Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
  • Cylinder
    cylinder The cylinder surface is 922 dm2, its height is equal to the radius of the base. Calculate height of this cylinder.
  • Hexagonal pyramid
    jehlan_6 Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
  • Body diagonal
    kvadr_diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
  • Sphere A2V
    sphere3 The surface of the sphere is 241 mm2. What is its volume?
  • 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 piece made a cube. In what ratio are the surfaces of these cubes?
  • Squares ratio
    squares2 The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte