density of a sludge sample measured in the laboratory Given mass (m) = 46.0000 kg; volume (V) = 0.5030 m^3, determine the density (rho) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except rho is given, so isolate rho symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for rho:

   $$\rho = \dfrac{m}{V}$$

3. Step 3

   $$List the givens: mass (m) = 46.0000 kg, volume (V) = 0.5030 m^3$$

4. Step 4 — Substitute the given values:

   $$\rho = \dfrac{46.0000}{0.5030}$$

5. Step 5 — Evaluate:

   \rho = 91.4513\ \text{kg/m^3}

6. Step 6 — Check: returning rho = 91.4513 kg/m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 182.9 — kept a factor of two that cancels in the correct rearrangement.
• 45.7256 — dropped that same factor in the other direction.
• 100.6 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density of a soil or waste material sample Given volume (V) = 0.9810 m^3; density (rho) = 1,639 kg/m^3, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for m:

   $$m = \rho V$$

3. Step 3

   $$List the givens: volume (V) = 0.9810 m^3, density (rho) = 1,639 kg/m^3$$

4. Step 4 — Substitute the given values:

   $$m = 1639 0.9810$$

5. Step 5 — Evaluate:

   $$m = 1608\ \text{kg}$$

6. Step 6 — Check: returning m = 1,608 kg to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 3,216 — kept a factor of two that cancels in the correct rearrangement.
• 803.9 — dropped that same factor in the other direction.
• 1,769 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density calculation from measured mass and volume of a liquid sample Given mass (m) = 781.0 kg; density (rho) = 2,648 kg/m^3, determine the volume (V) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for V:

   $$V = \dfrac{m}{\rho}$$

3. Step 3

   $$List the givens: mass (m) = 781.0 kg, density (rho) = 2,648 kg/m^3$$

4. Step 4 — Substitute the given values:

   $$V = \dfrac{781.0}{2648}$$

5. Step 5 — Evaluate:

   V = 0.2949\ \text{m^3}

6. Step 6 — Check: returning V = 0.2949 m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.5899 — kept a factor of two that cancels in the correct rearrangement.
• 0.1475 — dropped that same factor in the other direction.
• 0.3244 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density of a sludge sample measured in the laboratory Given mass (m) = 346.0 kg; volume (V) = 0.2930 m^3, determine the density (rho) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except rho is given, so isolate rho symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for rho:

   $$\rho = \dfrac{m}{V}$$

3. Step 3

   $$List the givens: mass (m) = 346.0 kg, volume (V) = 0.2930 m^3$$

4. Step 4 — Substitute the given values:

   $$\rho = \dfrac{346.0}{0.2930}$$

5. Step 5 — Evaluate:

   \rho = 1181\ \text{kg/m^3}

6. Step 6 — Check: returning rho = 1,181 kg/m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,362 — kept a factor of two that cancels in the correct rearrangement.
• 590.4 — dropped that same factor in the other direction.
• 1,299 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density of a soil or waste material sample Given volume (V) = 0.9200 m^3; density (rho) = 701.0 kg/m^3, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for m:

   $$m = \rho V$$

3. Step 3

   $$List the givens: volume (V) = 0.9200 m^3, density (rho) = 701.0 kg/m^3$$

4. Step 4 — Substitute the given values:

   $$m = 701.0 0.9200$$

5. Step 5 — Evaluate:

   $$m = 644.9\ \text{kg}$$

6. Step 6 — Check: returning m = 644.9 kg to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,290 — kept a factor of two that cancels in the correct rearrangement.
• 322.5 — dropped that same factor in the other direction.
• 709.4 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density calculation from measured mass and volume of a liquid sample Given mass (m) = 941.0 kg; density (rho) = 2,999 kg/m^3, determine the volume (V) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for V:

   $$V = \dfrac{m}{\rho}$$

3. Step 3

   $$List the givens: mass (m) = 941.0 kg, density (rho) = 2,999 kg/m^3$$

4. Step 4 — Substitute the given values:

   $$V = \dfrac{941.0}{2999}$$

5. Step 5 — Evaluate:

   V = 0.3138\ \text{m^3}

6. Step 6 — Check: returning V = 0.3138 m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.6275 — kept a factor of two that cancels in the correct rearrangement.
• 0.1569 — dropped that same factor in the other direction.
• 0.3451 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density of a sludge sample measured in the laboratory Given mass (m) = 903.0 kg; volume (V) = 0.5420 m^3, determine the density (rho) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except rho is given, so isolate rho symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for rho:

   $$\rho = \dfrac{m}{V}$$

3. Step 3

   $$List the givens: mass (m) = 903.0 kg, volume (V) = 0.5420 m^3$$

4. Step 4 — Substitute the given values:

   $$\rho = \dfrac{903.0}{0.5420}$$

5. Step 5 — Evaluate:

   \rho = 1666\ \text{kg/m^3}

6. Step 6 — Check: returning rho = 1,666 kg/m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 3,332 — kept a factor of two that cancels in the correct rearrangement.
• 833.0 — dropped that same factor in the other direction.
• 1,833 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density of a soil or waste material sample Given volume (V) = 0.7660 m^3; density (rho) = 920.0 kg/m^3, determine the mass (m) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except m is given, so isolate m symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for m:

   $$m = \rho V$$

3. Step 3

   $$List the givens: volume (V) = 0.7660 m^3, density (rho) = 920.0 kg/m^3$$

4. Step 4 — Substitute the given values:

   $$m = 920.0 0.7660$$

5. Step 5 — Evaluate:

   $$m = 704.7\ \text{kg}$$

6. Step 6 — Check: returning m = 704.7 kg to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,409 — kept a factor of two that cancels in the correct rearrangement.
• 352.4 — dropped that same factor in the other direction.
• 775.2 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density calculation from measured mass and volume of a liquid sample Given mass (m) = 981.0 kg; density (rho) = 1,018 kg/m^3, determine the volume (V) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except V is given, so isolate V symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for V:

   $$V = \dfrac{m}{\rho}$$

3. Step 3

   $$List the givens: mass (m) = 981.0 kg, density (rho) = 1,018 kg/m^3$$

4. Step 4 — Substitute the given values:

   $$V = \dfrac{981.0}{1018}$$

5. Step 5 — Evaluate:

   V = 0.9637\ \text{m^3}

6. Step 6 — Check: returning V = 0.9637 m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1.9273 — kept a factor of two that cancels in the correct rearrangement.
• 0.4818 — dropped that same factor in the other direction.
• 1.0600 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density

density of a sludge sample measured in the laboratory Given mass (m) = 376.0 kg; volume (V) = 0.1250 m^3, determine the density (rho) in kg/m^3.

Start with the thinking

• The governing relation printed in this handbook section is Density.
• Everything except rho is given, so isolate rho symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Density of a material sample is mass per unit volume, a fundamental property used throughout environmental engineering calculations.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\rho = \dfrac{m}{V}$$

2. Step 2 — Rearrange symbolically for rho:

   $$\rho = \dfrac{m}{V}$$

3. Step 3

   $$List the givens: mass (m) = 376.0 kg, volume (V) = 0.1250 m^3$$

4. Step 4 — Substitute the given values:

   $$\rho = \dfrac{376.0}{0.1250}$$

5. Step 5 — Evaluate:

   \rho = 3008\ \text{kg/m^3}

6. Step 6 — Check: returning rho = 3,008 kg/m^3 to

   $$\rho = \dfrac{m}{V}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 6,016 — kept a factor of two that cancels in the correct rearrangement.
• 1,504 — dropped that same factor in the other direction.
• 3,309 — rounded an intermediate value before the final step.

Reference: FE Handbook — Density