The problems are on the density worksheet. Try them on your own first, then compare with the answers below.
Quick answer: Density is the mass of a material per unit of volume, found with the formula density = mass ÷ volume. These worked answers correct the 20 problems of the grade 6 science worksheet on density, from density basics to floating in the Dead Sea: each solution shows the formula, the substitution and the final answer with its unit.
Use these answers to check your working. Always write the formula first, then substitute the numbers with their units, then give the result. If your answer differs, look for a unit slip or a divided-the-wrong-way error.
Level: Grade 6 science (Year 7 · Class 6) · Curriculum: MS-PS1-2
Problem 2 Aluminium block
1. ρ = m ÷ V.2. 135 ÷ 50 = 2.7 g/cm³.
Problem 3 Cooking oil
1. m = ρ × V.2. 0.92 × 500 = 460 g.
Problem 4 Float or sink
Compare with 1.00 g/cm³.1. Floats.
2. Sinks.
3. Floats.
4. Sinks.
5. Floats.
Problem 5 Density units
1. 7.9 × 1000 = 7900 kg/m³.2. 920 ÷ 1000 = 0.92 g/cm³.
3. 2700 ÷ 1000 = 2.7 g/cm³.
Problem 6 Three objects in water
1. A and B float.2. C, since it sinks.
3. A: it floats higher, so more of it is above the surface and it is less dense.
Problem 7 Gold pendant
1. V = m ÷ ρ.2. 38.6 ÷ 19.3 = 2.0 cm³.
Problem 8 Density of a liquid
1. 164.0 − 92.0 = 72.0 g.2. 72.0 ÷ 80 = 0.90 g/cm³.
3. 0.90 is less than 1.00, so it floats.
Problem 9 Mass against volume
1. 81 g.2. 108 ÷ 40 = 2.7 g/cm³.
3. Yes, the density matches aluminium.
4. 2.7 × 25 = 67.5 g.
Problem 10 Two cubes
1. A: 790 ÷ 100 = 7.9 g/cm³; B: 270 ÷ 100 = 2.7 g/cm³.2. Cube A.
3. 7.9 ÷ 2.7 = 2.9 times.
Problem 11 Nail and ship
1. Steel is denser than water, and a solid nail has the density of steel, so it sinks.2. The hull encloses a large volume of air, so the average density of the whole ship is lower than that of water.
Problem 12 Layers in a jar
1. Top to bottom: paraffin, sunflower oil, water, corn syrup.2. It is denser than water but less dense than syrup, so it rests between the water and the corn syrup.
Problem 13 Concrete slab
1. 2.0 × 1.5 × 0.10 = 0.30 m³.2. 2400 × 0.30 = 720 kg.
Problem 14 Which metal?
1. Sample 1: 56.7 ÷ 21 = 2.7; sample 2: 89 ÷ 10 = 8.9; sample 3: 113 ÷ 10 = 11.3; sample 4: 39.5 ÷ 5 = 7.9 (all g/cm³).2. Aluminium, copper, lead and iron.
Problem 15 Egg in two liquids
1. It sinks in fresh water and floats in salt water.2. The egg is denser than fresh water but less dense than salt water.
3. 1.00 g/cm³ < ρ(egg) < 1.10 g/cm³.
4. Dissolved salt adds mass but only a little volume, so mass per volume increases.
Problem 16 Heavy means sinks?
1. 2.0 ÷ 0.80 = 2.5 g/cm³.2. It is more than 1.00 g/cm³, so it sinks.
3. The light pebble sinks and the heavy plank floats, so mass alone does not decide. Density decides.
Problem 17 Hollow iron ball
1. 600 ÷ 150 = 4.0 g/cm³.2. 4.0 is less than 7.9, so part of the ball must be empty.
3. 600 ÷ 7.9 = 75.9 cm³.
4. 150 − 75.9 = 74.1 cm³.
Problem 18 Mixing two liquids
1. X: 1.2 × 200 = 240 g; Y: 0.8 × 300 = 240 g.2. 480 g and 500 cm³.
3. 480 ÷ 500 = 0.96 g/cm³.
4. It is below 1.00, so it floats.
Problem 19 Floating ice
1. 460 ÷ 0.92 = 500 cm³.2. The displaced water has a mass of 460 g, so V = 460 ÷ 1.00 = 460 cm³.
3. 500 − 460 = 40 cm³.
4. 460 ÷ 500 × 100 = 92 %.
Problem 20 Floating in the Dead Sea
1. 60 × 1000 = 60 000 g.2. 60 000 ÷ 1.01 = 59 406 cm³ = 59.4 L.
3. 1.01 is below 1.24, so the body is less dense than the water.
4. 1.01 ÷ 1.24 = 0.815, so about 81 %.
