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Shortest Distance on Cube Surface

XAT 2023 · Quantitative Ability & Data Interpretation · Easy · Mensuration

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A non-flying ant wants to travel from the bottom corner to the diagonally opposite top corner of a cubical room. The side of the room is 2 meters. What will be the minimum distance that the ant needs to travel?

  1. A.

    6 meters

  2. B.

    (22+2)(2\sqrt{2} + 2) meters

  3. C.

    232\sqrt{3} meters

  4. D.

    262\sqrt{6} meters

  5. E.

    252\sqrt{5} meters

Answer

E

Explanation

Unfolding two adjacent faces of the cube gives a rectangle of dimensions 2 m×4 m2 \text{ m} \times 4 \text{ m}. Shortest distance = diagonal = 22+42=20=25\sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5} meters.

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