Solved Density Worksheet 1) An object has a density of 10.00 ... - Free Printable

Here is the step-by-step solution to all problems on the Density Worksheet.

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1) An object has a density of 10.00 g/mL. If the object has a volume of 25.00 mL, what is its mass?

Formula:
Density = Mass / Volume
→ Mass = Density × Volume

Calculation:
Mass = 10.00 g/mL × 25.00 mL = 250.00 g

✔ Answer: 250.00 g

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2) A metal cylinder has a mass of 6.20 g. The density of the cylinder is 21.0 g/mL. What is its volume?

Formula:
Density = Mass / Volume
→ Volume = Mass / Density

Calculation:
Volume = 6.20 g / 21.0 g/mL ≈ 0.295 mL

(We keep 3 significant figures since 6.20 has 3 and 21.0 has 3)

✔ Answer: 0.295 mL

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3) A rubber stopper has a mass of 4.27 g and a volume of 1.31 mL. What is its density?

Formula:
Density = Mass / Volume

Calculation:
Density = 4.27 g / 1.31 mL ≈ 3.26 g/mL

(We keep 3 significant figures — both values have 3 sig figs)

✔ Answer: 3.26 g/mL

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4) A metal cylinder is placed in a graduated cylinder which has been filled with water to the 70.0 mL mark. The water level rises to the 78.0 mL mark.

(a) What is the volume of the metal cylinder?

This uses the water displacement method.

Volume of cylinder = Final volume – Initial volume
= 78.0 mL – 70.0 mL = 8.0 mL

✔ Answer (a): 8.0 mL

(b) The cylinder has a density of 3.21 g/cm³. What is its mass?

Note: 1 cm³ = 1 mL → so volume = 8.0 cm³

Formula:
Mass = Density × Volume

Calculation:
Mass = 3.21 g/cm³ × 8.0 cm³ = 25.68 g

(We should report with 2 significant figures because 8.0 has 2 sig figs — though 3.21 has 3, the limiting factor is 8.0)

But typically in such problems, if 8.0 is written as 8.0 (with decimal), it implies 2 sig figs. However, many teachers accept 25.7 g or 26 g depending on context.

Strictly by sig fig rules: 8.0 has 2 sig figs → answer should be 26 g

But since 3.21 × 8.0 = 25.68, and 8.0 is likely intended as precise to 0.1, we can report as 25.7 g (rounded to one decimal place).

✔ Answer (b): 25.7 g *(or 26 g if strictly following 2 sig figs — but 25.7 is more accurate given the inputs)*

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5) A gold cube is 150.00 mm long, 10.00 cm wide, and 0.95 mm thick. If gold has a density of 19.3 g/cm³, calculate the mass of the gold cube.

Step 1: Convert all dimensions to same unit — cm

- Length: 150.00 mm = 15.000 cm (since 10 mm = 1 cm)
- Width: 10.00 cm → already in cm
- Thickness: 0.95 mm = 0.095 cm

Step 2: Calculate volume

Volume = Length × Width × Height
= 15.000 cm × 10.00 cm × 0.095 cm = 14.25 cm³

Step 3: Calculate mass

Mass = Density × Volume
= 19.3 g/cm³ × 14.25 cm³ = 275.025 g

Now consider significant figures:

- 19.3 has 3 sig figs
- 15.000 has 5
- 10.00 has 4
- 0.95 has 2 sig figs ← this limits the precision!

So final answer should have 2 sig figs

→ 275.025 g → rounds to 280 g

✔ Answer: 280 g

*(Note: Some might argue 0.95 has 2 sig figs, but it’s 9.5×10⁻¹ — so yes, 2 sig figs. So 280 g is correct.)*

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6) A rectangular fish tank is 60.00 cm long, 200.00 mm wide, and 200.00 m deep.

(a) What volume of water can it hold?

First, convert all units to cm for consistency.

- Length: 60.00 cm → already in cm
- Width: 200.00 mm = 20.000 cm (since 10 mm = 1 cm)
- Depth: 200.00 m = 200.00 × 100 cm = 20,000.00 cm

Volume = Length × Width × Height

= 60.00 cm × 20.000 cm × 20,000.00 cm
= 24,000,000 cm³

Or better expressed in liters or cubic meters:

Since 1 L = 1000 cm³ → 24,000,000 cm³ = 24,000 L

Also, 1 m³ = 1,000,000 cm³ → 24,000,000 cm³ = 24 m³

✔ Answer (a): 24,000,000 cm³ or 24 m³ or 24,000 L

(b) What is the mass of the water?

Density of water = 1.00 g/cm³ (standard value)

Mass = Density × Volume
= 1.00 g/cm³ × 24,000,000 cm³ = 24,000,000 g

Convert to kg: 24,000,000 g = 24,000 kg

Or since 1 L of water = 1 kg → 24,000 L = 24,000 kg

✔ Answer (b): 24,000 kg

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## ✔ Final Answers Summary:

1. 250.00 g
2. 0.295 mL
3. 3.26 g/mL
4. (a) 8.0 mL, (b) 25.7 g
5. 280 g
6. (a) 24,000,000 cm³ (or 24 m³), (b) 24,000 kg

Let me know if you’d like any step explained further!