SOLUTION: Fdocuments in science 8 density calculations 8 density ... - Free Printable

The image you've uploaded is a completed "Density Calculations Worksheet" for a Science 8 class, with all the problems solved and answers filled in. It appears to be a key or answer sheet, as the name "Key" is written at the top.

Let me walk through each problem and explain the solution process, verifying the calculations and ensuring correctness.

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🔷 Density Formula

The core formula used throughout is:

$$
\text{Density} (D) = \frac{\text{Mass} (m)}{\text{Volume} (V)}
$$

We can rearrange this to solve for mass or volume:
- $ m = D \times V $
- $ V = \frac{m}{D} $

Units are typically grams per cubic centimeter ($g/cm^3$) or grams per milliliter ($g/mL$), and since $1\,mL = 1\,cm^3$, these units are interchangeable.

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✔ Problem 1:

> A student measures the mass of an 8 cm³ block of brown sugar to be 12.9 g. What is the density?

Given:
- Mass $ m = 12.9\,g $
- Volume $ V = 8\,cm^3 $

$$
D = \frac{12.9}{8} = 1.6125\,g/cm^3
$$

✔ Answer: $ \boxed{1.6125\,g/cm^3} $ — Correct.

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✔ Problem 2:

> A chef fills a 50 mL container with 43.5 g of cooking oil. What is the density?

Given:
- Mass $ m = 43.5\,g $
- Volume $ V = 50\,mL $

$$
D = \frac{43.5}{50} = 0.87\,g/mL
$$

✔ Answer: $ \boxed{0.87\,g/mL} $ — Correct.

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✔ Problem 3:

> Calculate the mass of a liquid with a density of 2.5 g/mL and a volume of 15 mL.

Given:
- $ D = 2.5\,g/mL $
- $ V = 15\,mL $

$$
m = D \times V = 2.5 \times 15 = 37.5\,g
$$

✔ Answer: $ \boxed{37.5\,g} $ — Correct.

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✔ Problem 4:

> Calculate the volume of a liquid with a density of 5.45 g/mL and a mass of 65 g.

Given:
- $ D = 5.45\,g/mL $
- $ m = 65\,g $

$$
V = \frac{m}{D} = \frac{65}{5.45} \approx 11.93\,mL
$$

Wait — the handwritten answer says 11.93 mL, but the box shows 11.93 mL — correct.

But let's double-check:

$$
65 ÷ 5.45 ≈ 11.93\,mL
$$

✔ Answer: $ \boxed{11.93\,mL} $ — Correct.

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✔ Problem 5:

> A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube measures 4 cm, what is the density?

Step 1: Find volume of cube
- Side = 4 cm
- Volume $ V = s^3 = 4^3 = 64\,cm^3 $

Step 2: Use density formula
- $ m = 176\,g $
- $ V = 64\,cm^3 $

$$
D = \frac{176}{64} = 2.75\,g/cm^3
$$

✔ Answer: $ \boxed{2.75\,g/cm^3} $ — Correct.

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✔ Problem 6:

> A piece of cork displaces 23.5 mL of water. The mass of the cork is 5.7 g. What is the density?

Note: Displacement = volume of object = 23.5 mL

- $ m = 5.7\,g $
- $ V = 23.5\,mL $

$$
D = \frac{5.7}{23.5} \approx 0.2425\,g/mL
$$

But the answer is written as $ \boxed{0.24\,g/mL} $. This is rounded to two significant figures, which makes sense because both 5.7 and 23.5 have two significant figures.

So:
- $ 5.7 / 23.5 = 0.2425 \rightarrow 0.24\,g/mL $ (correct rounding)

✔ Answer: $ \boxed{0.24\,g/mL} $ — Correct.

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✔ Problem 7:

> A carver begins work on a block of granite weighing 2700 g. Dimensions: 20 cm × 10 cm × 5 cm.

Step 1: Volume
- $ V = L \times W \times H = 20 \times 10 \times 5 = 1000\,cm^3 $

Step 2: Density
- $ m = 2700\,g $
- $ V = 1000\,cm^3 $

$$
D = \frac{2700}{1000} = 2.7\,g/cm^3
$$

✔ Answer: $ \boxed{2.7\,g/cm^3} $ — Correct.

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✔ Problem 8:

> A piece of PVC pipe displaces 60 mL of water and has a mass of 78 g. What is its density?

- Volume $ V = 60\,mL $
- Mass $ m = 78\,g $

$$
D = \frac{78}{60} = 1.3\,g/mL
$$

✔ Answer: $ \boxed{1.3\,g/mL} $ — Correct.

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✔ Problem 9:

> A solid magnesium flare has a mass of 1300 g and a volume of 743 cm³. What is the density?

$$
D = \frac{1300}{743} \approx 1.75\,g/cm^3
$$

Check:
- $ 1300 ÷ 743 ≈ 1.749 → 1.75 $ (rounded to three significant figures)

✔ Answer: $ \boxed{1.75\,g/cm^3} $ — Correct.

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✔ Final Summary

All answers on the worksheet are correctly calculated and properly rounded based on significant figures and unit consistency.

| Problem | Answer | Correct? |
|--------|--------|---------|
| 1 | 1.6125 g/cm³ | ✔ |
| 2 | 0.87 g/mL | ✔ |
| 3 | 37.5 g | ✔ |
| 4 | 11.93 mL | ✔ |
| 5 | 2.75 g/cm³ | ✔ |
| 6 | 0.24 g/mL | ✔ |
| 7 | 2.7 g/cm³ | ✔ |
| 8 | 1.3 g/mL | ✔ |
| 9 | 1.75 g/cm³ | ✔ |

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📝 Key Takeaways:

- Always use $ D = \frac{m}{V} $ and rearrange as needed.
- Remember that $ 1\,mL = 1\,cm^3 $.
- Pay attention to significant figures when reporting final answers.
- For irregular objects, volume by displacement equals the volume of water displaced.

This worksheet is well-solved and serves as a great reference for understanding density calculations!

Let me know if you'd like a printable version or a study guide based on this!