What is the length of a diagonal of a cube with a side length of 10 cm? 200 cm 210cm 300 cm 320cm
2 answers
Question:
What is the length of a diagonal of a cube with a side length of 10 cm? 200 cm 210cm 300 cm 320cm
Answers
Answer:The length of the diagonal of the cube = √(3 × 10²) = √300 cmStep-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)
Answer:its c on endeguityStep-by-step explanation:
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