Question

An ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?

Answer 1

1. Along a diagonal, and then along an edge.

2. 48.28 cm.

Explanation:

Assume points A and B are at diagonally opposite corners, as in the diagram below.

1. Shortest path

The shortest path is to go along the diagonal AC and continue along the edge CB.

2. Distance

The distance travelled is

d = AC + CB

According to Pythagoras,

AC² = AD² + CD² = 20² + 20² = 400 + 400 = 800

AC = √800 = 20√2

d = AC + CB = 20√ 2+ 20 ≈ 2 × 1.414 + 20 = 48.28 cm

The ant travels 48.28 cm.