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.

Correct answer:

V =  12000 cm³
S =  3400 dm²
u₁ =  25 dm
u₂ =  42.72 dm
u₃ =  44.7214 dm
s =  47.1699 dm

Step-by-step explanation:

$$\begin{gathered} a=15\text{ cm } \\ b=20\text{ cm } \\ c=40\text{ cm } \\ V=a\cdot b\cdot c=15\cdot 20\cdot 40=12000{\text{cm}}^3 \end{gathered}$$

$S=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (15\cdot 20+20\cdot 40+40\cdot 15)=3400{\text{dm}}^2$

$u_1=\sqrt{a^2+b^2}=\sqrt{15^2+20^2}=25\text{ dm}$

$u_2=\sqrt{a^2+c^2}=\sqrt{15^2+40^2}=5\sqrt{73}=42.72\text{ dm}$

$u_3=\sqrt{b^2+c^2}=\sqrt{20^2+40^2}=20\sqrt{5}=44.7214\text{ dm}$

$s=\sqrt{a^2+b^2+c^2}=\sqrt{15^2+20^2+40^2}=5\sqrt{89}=47.1699\text{ dm}$

Try another example

Related math problems and questions:

• 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.
• Block or cuboid
  The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
• Wall and body diagonals
  Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
• Body diagonal - cube
  Calculate the surface and cube volume with body diagonal 15 cm long.
• Body diagonal
  Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
• Wall and body diagonals
  The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
• Space diagonal angles
  Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
• Cube diagonals
  Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
• 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.
• Body diagonal
  The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
• Cuboid diagonal
  Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, c has dimensions in the ratio of 9:3:8. If you know that the diagonal wall AC is 86 cm, and the angle between AC and space diagonal AG is 25 degrees.
• 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
• Cube diagonals
  The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
• Regular hexagonal prism
  Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• Cuboid easy
  The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
• Solid cuboid
  A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.