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Density worksheet

Grades 8–9 · CCSS HSG.MG.A.2

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Mass
- Density (ρ): 3.8 g/cm³
- Volume (V): 1 L
- Show mass in: Kilograms (kg)
Find: Mass
Answer
2.
Problem 2.
- Solve for: Mass
- Density (ρ): 2.1 g/cm³
- Volume (V): 1 L
- Show mass in: Grams (g)
Find: Mass
Answer
3.
Problem 3.
- Solve for: Density
- Mass (m): 2.4 kg
- Volume (V): 1 L
- Show density in: Kilograms per cubic meter (kg/m³)
Find: Density
Answer
4.
Problem 4.
- Solve for: Volume
- Density (ρ): 3.2 g/cm³
- Mass (m): 2.4 kg
- Show volume in: Cubic meters (m³)
Find: Volume
Answer
5.
Problem 5.
- Solve for: Mass
- Density (ρ): 2.7 g/cm³
- Volume (V): 1 L
- Show mass in: Kilograms (kg)
Find: Mass
Answer
6.
Problem 6.
- Solve for: Density
- Mass (m): 2.6 kg
- Volume (V): 2 L
- Show density in: Pounds per cubic foot (lb/ft³)
Find: Density
Answer
7.
Problem 7.
- Solve for: Volume
- Density (ρ): 2.2 g/cm³
- Mass (m): 3.6 kg
- Show volume in: Cubic feet (ft³)
Find: Volume
Answer
8.
Problem 8.
- Solve for: Density
- Mass (m): 3.3 kg
- Volume (V): 1 L
- Show density in: Pounds per cubic foot (lb/ft³)
Find: Density
Answer
9.
Problem 9.
- Solve for: Mass
- Density (ρ): 2.6 g/cm³
- Volume (V): 1 L
- Show mass in: Grams (g)
Find: Mass
Answer
10.
Problem 10.
- Solve for: Density
- Mass (m): 2.7 kg
- Volume (V): 1 L
- Show density in: Kilograms per cubic meter (kg/m³)
Find: Density
Answer

Answer key: Density worksheet

1. Mass: 3.8 kg
1. Change the density to kg/m³ so all the units match before using the formula (1 g/cm³ = 1,000 kg/m³)
  $3.8 g/cm³ \times 1,000$ $= 3,800 kg/m³$
2. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
3. Multiply the density by the volume to get the mass
  $3,800 \times 0.001$ $= 3.8 kg$
2. Mass: 2,100 g
1. Change the density to kg/m³ so all the units match before using the formula (1 g/cm³ = 1,000 kg/m³)
  $2.1 g/cm³ \times 1,000$ $= 2,100 kg/m³$
2. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
3. Multiply the density by the volume to get the mass
  $2,100 \times 0.001$ $= 2.1 kg$
4. Change the answer to g, the unit you picked, by dividing by 0.001
  $\frac{2.1}{0.001}$ $= 2,100 g$
3. Density: 2,400 kg/m³
1. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
2. Divide the mass by the volume to get the density
  $\frac{2.4}{0.001}$ $= 2,400 kg/m³$
4. Volume: 7.5e-4 m³
1. Change the density to kg/m³ so all the units match before using the formula (1 g/cm³ = 1,000 kg/m³)
  $3.2 g/cm³ \times 1,000$ $= 3,200 kg/m³$
2. Divide the mass by the density to get the volume
  $\frac{2.4}{3,200}$ $= 0.00075 m³$
5. Mass: 2.7 kg
1. Change the density to kg/m³ so all the units match before using the formula (1 g/cm³ = 1,000 kg/m³)
  $2.7 g/cm³ \times 1,000$ $= 2,700 kg/m³$
2. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
3. Multiply the density by the volume to get the mass
  $2,700 \times 0.001$ $= 2.7 kg$
6. Density: 81.16 lb/ft³
1. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $2 L \times 0.001$ $= 0.002 m³$
2. Divide the mass by the volume to get the density
  $\frac{2.6}{0.002}$ $= 1,300 kg/m³$
3. Change the answer to lb/ft³, the unit you picked, by dividing by 16.01846337396
  $\frac{1,300}{16.01846337396}$ $= 81.156349 lb/ft³$
7. Volume: 0.06 ft³
1. Change the density to kg/m³ so all the units match before using the formula (1 g/cm³ = 1,000 kg/m³)
  $2.2 g/cm³ \times 1,000$ $= 2,200 kg/m³$
2. Divide the mass by the density to get the volume
  $\frac{3.6}{2,200}$ $= 0.001636 m³$
3. Change the answer to ft³, the unit you picked, by dividing by 0.028316846592
  $\frac{0.001636}{0.028316846592}$ $= 0.057788 ft³$
8. Density: 206.01 lb/ft³
1. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
2. Divide the mass by the volume to get the density
  $\frac{3.3}{0.001}$ $= 3,300 kg/m³$
3. Change the answer to lb/ft³, the unit you picked, by dividing by 16.01846337396
  $\frac{3,300}{16.01846337396}$ $= 206.01227 lb/ft³$
9. Mass: 2,600 g
1. Change the density to kg/m³ so all the units match before using the formula (1 g/cm³ = 1,000 kg/m³)
  $2.6 g/cm³ \times 1,000$ $= 2,600 kg/m³$
2. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
3. Multiply the density by the volume to get the mass
  $2,600 \times 0.001$ $= 2.6 kg$
4. Change the answer to g, the unit you picked, by dividing by 0.001
  $\frac{2.6}{0.001}$ $= 2,600 g$
10. Density: 2,700 kg/m³
1. Change the volume to m³ so all the units match before using the formula (1 L = 0.001 m³)
  $1 L \times 0.001$ $= 0.001 m³$
2. Divide the mass by the volume to get the density
  $\frac{2.7}{0.001}$ $= 2,700 kg/m³$