Density practice problems worksheet featuring formulas and calculations for volume and density.

Let's solve each problem step by step using the density formula and the information provided.

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Problem 1: Platinum Bar

Given:
- Length = 5.0 cm
- Width = 4.0 cm
- Thickness (height) = 1.5 cm
- Mass = 700.0 grams

#### a. Calculate the volume of the platinum bar.

The platinum bar is a rectangular prism, so its volume is calculated as:

$$
V = \text{length} \times \text{width} \times \text{thickness}
$$

$$
V = 5.0\, \text{cm} \times 4.0\, \text{cm} \times 1.5\, \text{cm}
$$

$$
V = 30.0\, \text{cm}^3
$$

✔ Volume = 30.0 cm³

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#### b. Calculate the density of the platinum bar.

Use the density formula:

$$
\text{Density} = \frac{\text{mass}}{\text{volume}} = \frac{m}{V}
$$

$$
d = \frac{700.0\, \text{g}}{30.0\, \text{cm}^3} = 23.33\, \text{g/cm}^3
$$

✔ Density = 23.3 g/cm³ (rounded to one decimal place)

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Problem 2: Lead Cylinder

Given:
- Mass = 540 grams
- Density = 2.70 g/mL

We need to find the volume.

Use the rearranged density formula:

$$
V = \frac{m}{d}
$$

$$
V = \frac{540\, \text{g}}{2.70\, \text{g/mL}} = 200\, \text{mL}
$$

✔ Volume = 200 mL

> Note: 1 mL = 1 cm³, so this is also 200 cm³.

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✔ Final Answers:

1a. Volume of platinum bar = 30.0 cm³
1b. Density of platinum bar = 23.3 g/cm³
2. Volume of lead cylinder = 200 mL

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🔍 Explanation Summary:

- Volume of a rectangular solid = length × width × height.
- Density = mass ÷ volume → use the triangle method (cover what you want).
- For unknown volume, rearrange: $ V = m/d $

These problems reinforce understanding of the relationship between mass, volume, and density.