Longest rod and shortest ant path in a box
Longest rod and shortest ant path in a box
IP 2
7 marks
A closed box is a cuboid measuring \(30\) cm by \(40\) cm by \(120\) cm. \(P\) and \(Q\) are opposite corners of the box.
- Find the length of the longest straight thin rod that fits inside the box.[2]
- An ant walks from \(P\) to \(Q\) along the outside surface of the box. By unfolding two faces into a flat net, find the length of the shortest possible path, giving your answer correct to \(3\) significant figures. Explain why there are three paths to compare.[5]
Solution:
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Answer:(a) \(130\text{ cm}\) (b) \(139\text{ cm}\) (3 s.f.); the crossed edge can be any of the three edge directions, giving \(\sqrt{19300}\), \(\sqrt{24100}\), \(\sqrt{26500}\)
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