4 + 3 + 7 to the 3rd power
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Answer:
The length of the diagonal of the cube = √(3 × 10²) = √300 cm
Step-by-step explanation:
* Lets revise the properties of the cube
- It has six equal faces all of them are squares
- It has 12 vertices
- The diagonal of the cube is the line joining two vertices in opposite
faces (look to the attached figure)
- To find the length of the diagonal do that:
# Find the diagonal of the base using Pythagoras theorem
∵ The length of the side of the cube is L
∵ The base is a square
∴ The length of the diagonal d = √(L² + L²) = √(2L²)
- Now use the diagonal of the base and a side of a side face to find the
diagonal of the cube by Pythagoras theorem
∵ d = √(2L²)
∵ The length of the side of the square = L
∴ The length of the diagonal of the cube = √[d² + L²]
∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root
∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)
* Now lets solve the problem
∵ The length of the side of the square = 10 cm
∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm
- Note: you can find the length of the diagonal of any cube using
this rule Diagonal = √(3L²)
