block of metal is 1.84 cm long, 1.71 cm wide and 7.59 high. it has a mass of 201.3 grams. what is the density of the metal

To calculate the density of the metal, we use the formula:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

### Step 1: Calculate the volume of the metal block.
The volume \( V \) of a rectangular block is calculated by multiplying its length, width, and height:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

Given:
- Length = 1.84 cm
- Width = 1.71 cm
- Height = 7.59 cm

\[
V = 1.84 \, \text{cm} \times 1.71 \, \text{cm} \times 7.59 \, \text{cm} = 23.901336 \, \text{cm}^3
\]

### Step 2: Calculate the density.
Now, using the mass of the block (201.3 grams) and the volume calculated:

\[
\text{Density} = \frac{201.3 \, \text{g}}{23.901336 \, \text{cm}^3} \approx 8.42 \, \text{g/cm}^3
\]

### Final Answer:
The density of the metal is approximately \( 8.42 \, \text{g/cm}^3 \).

Would you like more details, or do you have any questions?

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Here are 5 related questions:
1. What happens to the density if the mass of the metal block is doubled?
2. How would the density change if the dimensions of the block are halved but the mass remains constant?
3. Can the density of an irregular object be calculated in a similar way?
4. How is density related to the buoyancy of an object in water?
5. What are common metals that have a density close to 8.42 g/cm³?

**Tip**: Density is a characteristic property of a material, meaning it can be used to identify the type of metal.

A block of metal is 1.84 cm long, 1.71 cm wide, and 7.59 cm high. It has a mass of 201.3 grams. What is the density of the metal?

Learn how to calculate the density of a metal block with dimensions of 1.84 cm × 1.71 cm × 7.59 cm and a mass of 201.3 grams. The detailed step-by-step solution includes volume calculation and the formula for density. Suitable for students in Grades 6-8.

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