Math Problem Statement

Diketahui kubus PQRS.TUVW dengan panjang rusuk 6 cm. Jarak antara titik P ke titik W adalah?

Solution

The problem describes a cube PQRS.TUVWPQRS.TUVW with a side length of 6cm6 \, \text{cm}. We need to find the distance between points PP and WW.

Solution:

  1. Visualize the Cube:

    • PP is at one vertex of the cube.
    • WW is at the vertex diagonally opposite to PP across the entire cube.
  2. Apply the 3D Diagonal Formula: The formula to calculate the space diagonal dd of a cube is: d=3ad = \sqrt{3} \cdot a where aa is the side length of the cube.

  3. Substitute the Values: a=6cma = 6 \, \text{cm} d=36cm=63cmd = \sqrt{3} \cdot 6 \, \text{cm} = 6\sqrt{3} \, \text{cm}

  4. Calculate the Numerical Value: If you need an approximate decimal value: 636×1.73210.39cm6\sqrt{3} \approx 6 \times 1.732 \approx 10.39 \, \text{cm}

So, the distance between point PP and point WW is 63cm6\sqrt{3} \, \text{cm} or approximately 10.39cm10.39 \, \text{cm}.

Would you like more details or have any other questions? Here are some related questions to consider:

  1. How do you derive the formula for the space diagonal of a cube?
  2. What would be the distance between two adjacent vertices of the cube?
  3. How does the distance between the cube's vertices change if the side length is doubled?
  4. Can you use the Pythagorean theorem to find the distance between two vertices in a cube?
  5. What are some real-life applications of calculating distances in 3D objects?

Tip: In a cube, the space diagonal is always 3\sqrt{3} 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