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.

Correct answer:

a =  16 cm
b =  32 cm
c =  48 cm

Step-by-step explanation:

$$\begin{gathered} V=24576{\text{cm}}^3 \\ a:b:C=2:4:6 \\ V=abc \\ V=2k\cdot 4k\cdot 6k=48k^3 \\ k=\sqrt[3]{V\mathrm{/}48}=\sqrt[3]{24576\mathrm{/}48}=8\text{ cm } \\ a=2\cdot k=2\cdot 8=16\text{ cm} \end{gathered}$$

$b=4\cdot k=4\cdot 8=32\text{ cm}$

$c=6\cdot k=6\cdot 8=48\text{ cm}$

Try another example

Related math problems and questions:

• Cuboid and ratio
  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
• Prism X
  The prism with the edges of the lengths x cm, 2x cm, and 3x cm has volume 20250 cm³. What is the area of the surface of the prism?
• 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.
• Cuboid face diagonals
  The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
• Ratio-cuboid
  The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
• Cube 7
  Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
• Cuboid - edges
  The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
• Uboid volume
  Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
• Ratio of edges
  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.
• Edges or sides
  Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
• Magnified cube
  If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube.
• Regular square prism
  The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism.
• Cuboid edges
  The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m².
• 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.
• Cuboid
  The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
• Three cubes
  Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge?
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?