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K. 142. In the Mathematical Olympiad of 2100, gold and silver medals will be made of pure gold and silver (and bronze medals will be made of bronze). The diameter of the silver medal will be 3 cm, with a thickness of 5 mm. (The shape of the medals will be as usual.) What will be the diameters of the gold and bronze medals if all the three kinds of medal have the same mass and thickness? (Densities: gold 19\;300~\rm kg/m^{3}, silver 10\;500~\rm kg/m^{3}, bronze 8930 kg/m3.)

(6 points)

This problem is for grade 9 students only.

Deadline expired on 10 December 2007.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: Az ezüstérem tömege me=0,0152.\pi.0,005.10500\approx0,037 kg. Ugyanilyen tömegű aranyérem térfogata 0,037 kg=ra2.\pi.0,005.19300, amiből az aranyérem sugara kb. 0,011 m. Hasonlóan a bronzéremre 0,037 kg=rb2.\pi.0,005.8930, ahonnan a bronzérem sugara kb. 0,016 m.

Statistics on problem K. 142.
212 students sent a solution.
6 points:115 students.
5 points:35 students.
4 points:18 students.
3 points:14 students.
2 points:8 students.
1 point:7 students.
0 point:4 students.
Unfair, not evaluated:6 solutions.
Unfair, not evaluated:5 solutions.

  • Problems in Mathematics of KöMaL, November 2007

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