# Density + unit conversion - math problems

1. Copper Cu wire Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
2. The water tank The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
3. AL wire What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.
4. Oak trunk Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.
5. Cone from cube The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3
6. The copper wire The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
7. Wall thickness The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
8. Aquarium Try to estimate the weight of the water in an aquarium 50cm long 30cm wide, when poured to a height of 25cm. Calculates the weight of the aquarium's water.
9. The prison ball Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.
10. Heptagonal pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.
11. Cheops pyramid The Pyramid of Cheops is a pyramid with a square base with a side of 233 m and a height of 146.6 m. It made from limestone with a density of 2.7 g/cm3. Calculate the amount of stone in tons. How many trains with 30 twenty tons wagons carry the stone?
12. Wood prisms How many weight 25 prisms with dimensions 8x8x200 cm? 1 cubic meter of wood weighs 800 kg.
13. The glass 1 m3 of glass weighs 2600 kg. Calculate the weight of the glass glazing panel with dimensions of 2.5 m and 3.8 m if the thickness of the glass is 0.8 cm
14. Steel tube The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.
15. Metal tube Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
16. Castle model The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm2 of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of wo
17. Iron ball The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
18. Iron density Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
19. Orlík hydroelectric plant The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the
20. Gold horseshoe Calculate the volume of a gold horseshoe that weighs 750g.

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