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

Correct result:

a =  6 cm
b =  9 cm
c =  15 cm

Solution:

$$\begin{gathered} a=2x \\ b=3x \\ c=5x \\ V=810{\text{cm}}^3 \\ V=abc=2\cdot 3\cdot 5x^3 \\ x=\sqrt[3]{V\mathrm{/}(2\cdot 3\cdot 5)}=\sqrt[3]{810\mathrm{/}(2\cdot 3\cdot 5)}=3\text{ cm } \\ a=2\cdot x=2\cdot 3=6\text{ cm} \end{gathered}$$

$b=3\cdot x=3\cdot 3=9\text{ cm}$

$c=5\cdot x=5\cdot 3=15\text{ cm}$

Try another example

Showing 0 comments:

Next similar math problems:

• 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.
• 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
• 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.
• 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.
• 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.
• 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.
• 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.
• 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?
• Cube 7
  Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
• Edges or sides
  Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
• Transforming cuboid
  Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
• Cuboid height
  What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
• Cuboid walls
  If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
• Cube surface and volume
  The surface of the cube is 500 cm², how much cm³ will be its volume?
• Rectangular cuboid
  The rectangular cuboid has a surface area 5334 cm², and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
• Cuboid - ratio
  Find the volume of a block whose dimensions are in the ratio 2: 3: 4 and the surface is 117 dm².
• Uboid volume
  Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²