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.

Correct result:

V =  2514.3938 cm³

Solution:

$$\begin{gathered} u=28\text{ cm } \\ a=3x \\ b=1x \\ c=2x \\ u=\sqrt{a^2+b^2+c^2} \\ {u}^2=(9+1+4)x^2 \\ x=\sqrt{{\displaystyle \frac{u^2}{9+1+4}}}=\sqrt{{\displaystyle \frac{28^2}{9+1+4}}}=2\sqrt{14}\text{ m}\doteq 7.4833\text{ m } \\ a=3\cdot x=3\cdot 7.4833=6\sqrt{14}\text{ m}\doteq 22.4499\text{ m } \\ b=x=7.4833=2\sqrt{14}\text{ m}\doteq 7.4833\text{ m } \\ c=2\cdot x=2\cdot 7.4833=4\sqrt{14}\text{ m}\doteq 14.9666\text{ m } \\ V=a\cdot b\cdot c=22.4499\cdot 7.4833\cdot 14.9666=2514.3938{\text{cm}}^3 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Here is
  Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
• 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.
• Cuboid diagonals
  The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
• Faces diagonals
  If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
• Rhombus and diagonals
  The a rhombus area is 150 cm² and the ratio of the diagonals is 3:4. Calculate the length of its height.
• Body 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
• ISO triangle
  Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The heig
• Cube diagonals
  Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
• The tent
  The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent?
• Right triangle - ratio
  The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
• Cone side
  Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
• Regular hexagonal prism
  Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• A rectangle 2
  A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
• Axial section of the cone
  The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
• Cube in a sphere
  The cube is inscribed in a sphere with volume 7253 cm³. Determine the length of the edges of a cube.
• Nice prism
  Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.