Answer key for Density Practice Problems Worksheet #2, showing step-by-step solutions for calculating density, mass, and volume using various formulas and examples.

You’ve uploaded an answer key for a “Density Practice Problems Worksheet #2,” which already contains the solved problems and explanations. Since you asked to “solve the problem and explain the solution,” I’ll walk through each problem step by step, explaining the concepts and calculations clearly — even though the answers are already shown in red.

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🔹 Problem 1:

> You have a rock with a volume of 15 cm³ and a mass of 45 g. What is its density?

✔ Solution:

Formula:
Density = Mass ÷ Volume → D = m / V

Plug in the values:
D = 45 g / 15 cm³ = 3.0 g/cm³

📌 Explanation:
Density tells us how much mass is packed into a given volume. Here, every cubic centimeter of this rock contains 3 grams of mass.

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🔹 Problem 2:

> You have a different rock with a volume of 30 cm³ and a mass of 60 g. What is its density?

✔ Solution:

D = m / V = 60 g / 30 cm³ = 2.0 g/cm³

📌 Explanation:
Even though this rock has more mass (60g vs 45g), it also takes up more space (30 cm³ vs 15 cm³), so its density is lower — meaning it’s less tightly packed with matter.

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🔹 Problem 3:

> In the above two examples, which rock is more dense? Why?

✔ Solution:

Rock #1 is more dense because its density is 3.0 g/cm³, which is greater than Rock #2’s 2.0 g/cm³.

📌 Explanation:
Density is a measure of how compact or “heavy for its size” a material is. Even if something is larger or heavier overall, if it spreads that mass over more volume, it’s less dense. Rock #1 packs more mass into less space → higher density.

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🔹 Problem 4:

> Calculate the mass of a liquid with a density of 3.2 g/mL and a volume of 25 mL.

✔ Solution:

We rearrange the density formula:
Mass = Density × Volume → m = D × V

m = 3.2 g/mL × 25 mL = 80.0 g

📌 Explanation:
Since 1 mL = 1 cm³, we can treat mL and cm³ as equivalent for water-like substances. Multiplying density (mass per unit volume) by total volume gives total mass.

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🔹 Problem 5:

> Calculate the density of a 500g rectangular block with dimensions: length=8 cm, width=6 cm, height=5 cm.

✔ Solution:

First, find volume:
V = length × width × height = 8 cm × 6 cm × 5 cm = 240 cm³

Then use D = m / V = 500 g / 240 cm³ ≈ 2.083 g/cm³

Rounded to the nearest tenth → 2.1 g/cm³

📌 Explanation:
For regular shapes like rectangles, volume is calculated by multiplying the three dimensions. Then plug into the density formula. Rounding follows standard rules: look at the hundredths place (8 ≥ 5), so round up the tenths place from 0 to 1.

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🔹 Problem 6:

> Calculate the mass of a solid metal block with a density of 2.6 g/cm³, width=1.8 cm, length=4 cm, height=2.3 cm.

✔ Solution:

First, find volume:
V = 1.8 cm × 4 cm × 2.3 cm = 16.56 cm³

Then use m = D × V = 2.6 g/cm³ × 16.56 cm³ = 43.056 g

Rounded to nearest tenth → 43.1 g

📌 Explanation:
Again, calculate volume using the three dimensions. Multiply by density to get mass. When rounding 43.056 to the nearest tenth, look at the hundredths digit (5), which means we round up the tenths digit (0 → 1).

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## ✔ Summary of Key Concepts:

- Density Formula: D = m / V
- Mass Formula: m = D × V
- Volume for Rectangular Solids: V = l × w × h
- Units Matter! g/cm³ and g/mL are often interchangeable for liquids/solids near water’s density.
- Rounding Rules: Look at the digit after the place you’re rounding to — if ≥5, round up.

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## 🧠 Bonus Tip:
Density helps identify materials! For example:
- Water = 1.0 g/cm³
- Aluminum ≈ 2.7 g/cm³
- Iron ≈ 7.9 g/cm³
So if you calculate a density close to one of these, you might guess what the material is!

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