Question

An iron block has a length of 8 cm, a width of 5 cm, and a height of 4 cm. If the density of iron is 7,874 kg/m3 , which of the following correctly calculates the mass of the block?

(1 point)
Responses

1,259,840 g
1,259,840 g

49.2125 g
49.2125 g

1,259.84 g
1,259.84 g

0.49 g

Answer 1

To calculate the mass of the iron block, you can use the formula:

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

1. **Calculate the volume of the block**:
The volume \( V \) of a rectangular prism (block) is calculated as:

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

Given:
- Length = 8 cm = 0.08 m (you need to convert cm to m)
- Width = 5 cm = 0.05 m
- Height = 4 cm = 0.04 m

Now calculate the volume in cubic meters:

\[
V = 0.08 \, \text{m} \times 0.05 \, \text{m} \times 0.04 \, \text{m} = 0.00016 \, \text{m}^3
\]

2. **Use the density to find the mass**:
Given the density of iron is 7,874 kg/m³:

\[
\text{Mass} = 0.00016 \, \text{m}^3 \times 7,874 \, \text{kg/m}^3 = 1.2624 \, \text{kg}
\]

3. **Convert kilograms to grams**:
To convert kilograms to grams, multiply by 1,000:

\[
1.2624 \, \text{kg} \times 1,000 \, \text{g/kg} = 1,262.4 \, \text{g}
\]

Now to summarize, the mass of the iron block is approximately 1,262.4 g. Since the options provided were:

- 1,259,840 g
- 49.2125 g
- 1,259.84 g
- 0.49 g

None of the options exactly match the calculated mass. However, the closest option provided is **1,259.84 g**.

Therefore, the correct response is:

**1,259.84 g**.