Mathematics

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• Winch
  The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
• Sphere floating
  Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
• Delayed clock
  Michael put a new battery into his watch at midnight. However, they are 5 seconds late each minute. How many hours does the watch show in 24 hours?
• Iceberg
  What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
• Banknotes
  How many different ways can the cashier payout € 310 if he uses only 50 and 20 euro banknotes? Find all solutions.
• Concentric circles
  There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
• Number of songs
  Write an expression for the number of songs they need for this show. Evan and Peter have a radio show that has 2 parts. They need 4 fewer than 11 songs in the first part. In the second part, they need 5 fewer than 3 times the number of songs in the first p

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