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Traffic Tunnel

Age 14 to 16 Short Challenge Level:

A traffic tunnel is being planned. The diagram shows the cross-section of the tunnel. The shape of the tunnel is the same as the graph of $y=\frac49(9-x^2)$.
All distances are in metres.

Which of these vehicles will fit through the tunnel?

a) truck, 2.9 m high, 4 m wide
b) coach, 3.4 m high, 3 m wide
c) lorry, 3.9 m high, 2 m wide

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.