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 l
ong will it be (in cm)?
1 answer:
Answer:
1. Along a diagonal, and then along an edge.
2. 48.28 cm.
Step-by-step 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.
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