Math Problem Statement
Solution
The problem describes a cube with a side length of . We need to find the distance between points and .
Solution:
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Visualize the Cube:
- is at one vertex of the cube.
- is at the vertex diagonally opposite to across the entire cube.
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Apply the 3D Diagonal Formula: The formula to calculate the space diagonal of a cube is: where is the side length of the cube.
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Substitute the Values:
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Calculate the Numerical Value: If you need an approximate decimal value:
So, the distance between point and point is or approximately .
Would you like more details or have any other questions? Here are some related questions to consider:
- How do you derive the formula for the space diagonal of a cube?
- What would be the distance between two adjacent vertices of the cube?
- How does the distance between the cube's vertices change if the side length is doubled?
- Can you use the Pythagorean theorem to find the distance between two vertices in a cube?
- What are some real-life applications of calculating distances in 3D objects?
Tip: In a cube, the space diagonal is always times the side length. This is a quick way to find such distances!
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Math Problem Analysis
Mathematical Concepts
Geometry
3D Geometry
Cubes
Formulas
Space diagonal of a cube: d = sqrt(3) * a
Theorems
Pythagoras Theorem in 3D
Suitable Grade Level
Grades 9-10
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