Question

Maximum distance between any two points inside or on a cube of side 1 cm is equal to:

• A. 1 cm
• B. \( \sqrt{2} \, {cm} \)
• C. \( \sqrt{3} \, {cm} \)
• D. 6 cm

Hint:

The space diagonal of a cube is the maximum distance between any two points inside the cube, and it can be calculated using the formula \( \sqrt{3a^2} \), where \( a \) is the side length of the cube.

Answer 1

The Correct Option is C

Step 1: Understanding the problem.
We are given a cube with a side length of 1 cm, and we are asked to find the maximum distance between any two points inside or on the cube. The maximum distance between two points in a cube occurs when the two points are at opposite corners of the cube. 
Step 2: Applying the Pythagorean Theorem in 3D.
The maximum distance between two points inside the cube is the space diagonal of the cube, which connects two opposite corners. The space diagonal, \( d \), of a cube with side length \( a \) is given by the formula: \[ d = \sqrt{a^2 + a^2 + a^2} = \sqrt{3a^2} = a\sqrt{3} \] For a cube with a side length of 1 cm: \[ d = 1 \times \sqrt{3} = \sqrt{3} \, {cm} \] Step 3: Conclusion.
Thus, the maximum distance between two points inside or on the cube is \( \sqrt{3} \, {cm} \). Therefore, the correct answer is (3) \( \sqrt{3} \, {cm} \).