Student's handwritten answers to a worksheet on calculating density using the formula density = mass/volume, with problems involving different materials and units.

Let's go through each problem step by step and verify the solutions. The key formula for density is:

$$
\text{Density} = \frac{\text{Mass}}{\text{Volume}} \quad \text{or} \quad \rho = \frac{m}{V}
$$

We can rearrange this formula as needed:
- $ m = \rho \times V $
- $ V = \frac{m}{\rho} $

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

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

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

Rounded to two decimal places: 1.61 g/cm³

✔ Your answer: 1.61 g/cm³ — Correct

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

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

Note: 1 mL = 1 cm³, so units are compatible.

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

✔ Your answer: 0.87 g/mL — Correct

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

Given:
- Density $ \rho = 2.5 \, \text{g/mL} $
- Volume $ V = 15 \, \text{mL} $

$$
m = \rho \times V = 2.5 \, \text{g/mL} \times 15 \, \text{mL} = 37.5 \, \text{g}
$$

✔ Your answer: 37.5 g — Correct

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

Given:
- $ m = 65 \, \text{g} $
- $ \rho = 5.45 \, \text{g/mL} $

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

✔ Your answer: 11.93 mL — Correct

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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 of the aluminum?

First, find the volume of the cube:

$$
V = \text{side}^3 = 4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm} = 64 \, \text{cm}^3
$$

Now calculate density:

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

✔ Your answer: 2.75 g/cm³ — Correct

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6) A teacher performing a demonstration finds that a piece of cork displaces 23.5 mL of water. The piece of cork has a mass of 5.7 g. What is the density of the cork?

The displaced water volume equals the volume of the cork (by Archimedes' principle):

- Volume $ V = 23.5 \, \text{mL} = 23.5 \, \text{cm}^3 $
- Mass $ m = 5.7 \, \text{g} $

$$
\rho = \frac{5.7}{23.5} \approx 0.2426 \, \text{g/mL}
$$

Rounded to two significant figures (since 5.7 has two sig figs, and 23.5 has three), we use two sig figs:

$$
\rho \approx 0.24 \, \text{g/mL}
$$

⚠️ You didn't write an answer here in your image, but based on the calculation:

✔ Answer: 0.24 g/mL

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✔ Final Answers Summary:

1) 1.61 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

All your calculations are correct except for #6, which you left blank. The solution for #6 is 0.24 g/mL.

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