Density - practice problems - page 2 of 21
Why Does Density Matter?
1. Floating vs. Sinking:
- If an object’s density > liquid’s density → it sinks (e.g., iron in water).
- If density < liquid’s density → it floats (e.g., wood in water).
- *Example:* Ice ( ρ ≈ 0.92 g/cm³ ) floats on water ( ρ = 1 g/cm³ ).
2. Material Identification:
- Gold ( ρ = 19.3 g/cm³ ) vs. "fool’s gold" (pyrite, ρ = 5 g/cm³ ).
3. Engineering & Design:
- Ships are built with hollow shapes to reduce effective density.
- Lightweight materials (e.g., aluminum, ρ = 2.7 g/cm³ ) are used in aircraft.
Number of problems found: 402
- Density of a cube
Calculate the density of a cube if the height is 8 cm and the mass of the cube is 3 kg. - Iron rod
What is the mass of a cylindrical iron rod with a length a = 9 m and a diameter d = 6 cm? The density of iron is 7,800 kg/m³. Express the result in kilograms, and round to the nearest whole number. - Grass seed
How many kilograms of grass seed are needed to establish a lawn on a rhombus-shaped plot of land with sides 55m and 40m, if the height of the shorter side is 22m and 1kg of seed is enough for 40m square? - Detergent - dilution
The detergent is diluted in a ratio of 1:200. How much detergent do we need if we use 5 liters of water? - Aluminum - density
The density of aluminum is 2,700 kg/m³. Calculate the mass of an aluminum cube with a volume of 80 cm3! - Two-kilogram bread
Farmers harvested 3000 kg of rye from one hectare, from which they obtained 2500 kg of flour. 3 kg of flour will make 4 kg of bread. Calculate how many m² of land were used to grow rye, which is needed for 1 two-kilogram loaf of bread. - DEnsity of a cuboid
What is the density of a building board in the shape of a cuboid with dimensions 1 m, 20 cm, and 20 cm, if its mass is 84 kg? - Cylindrical column
What is the mass of a reinforced concrete cylindrical column with a radius of 30 cm and a height of 4.5 m if the density of reinforced concrete is 2400 kg/m³? Round the result to whole kilograms. - Atmospheric pressure
How and by how much hPa will the atmospheric pressure change when we take the cable car from Skalnate Pleso to Lomnický štít? The altitudes of the cable car stations are 1754 m above sea level and 2634 m above sea level. - Assume
Two naughty boys broke the glass on the front door. The glass was 105 cm, 150 cm, and 6 mm thick. They decided to buy the glass from their savings and, since they assumed that it would not weigh more than 12 kg, they would bring it and ask the caretaker t - Density of Titanium
The body of titanium weighs 227 kg and has a volume of 0.05 m³. What is its density? - Weight of Gasoline
The volume of the gasoline bottle is 15 liters. What is the weight of an entire bottle of petrol if the empty one weighs 1 kg? The density of gasoline is approximately 730 kg/m³. - Density of Cork
A cork stopper with a volume of 15 cm³ weighs 3 g. Determine the density of the cork. - Equilateral shell
The glass weight has the shape of a regular four-sided pyramid with a base edge of 10 cm. The shell walls are equilateral triangles. What is the weight in grams of the paperweight if the density of the glass is 2500 kg/m³? - Cost of Gasoline Refuel A liter of gasoline costs €1.2. After refueling, my car weight increased by 15 kg. The density of gasoline is p=750kg/m³. How many euros did I fill up with?
- Iron bar weight
Calculate the weight of an iron bar 1.2 m long, whose cross-section is a trapezoid with dimensions a=10 cm c=8 cm and the distance between the bases v=6 cm. As we know, 1 cubic meter of iron weighs 7800 kg. - Courtyard oak bricks The castle courtyard, with an area of 100 m², is paved with oak cubes with an edge of 8 cm. Approximately 164 bricks were used to pave m². One dm³ of oak wood weighs 0.8 kg. Calculate the weight of all the bricks used to pave the courtyard.
- Milk butter kilograms
8 kg of butter is made from 20 hl of milk. How many kilograms of butter can be made from 450 l of milk? - Steel rope weight
Calculate the weight in kg of a steel rope 1.5 cm in diameter and 10 m long if one cubic centimeter of steel weighs 7.8 g - Boat cargo increase
A cargo boat with a total weight of 4,500t sailed from the river to the sea. Calculate by how many tons it is possible to increase the weight of the cargo on the boat at sea so that the draft remains the same as in the river. The density of river water is
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