Question

An iron block has a length of 8 centimeters, a width of 5 centimeters, and a height of 4 centimeters. 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

1,259.84 g
1,259.84 g

49.2125 g
49.2125 g

0.49 g

Answer 1

To calculate the mass of the iron block, we first need to find its volume and then use the density to find the mass.

1. **Calculate the volume of the block:**
The volume \( V \) of a rectangular block is given by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

Given:
- Length = 8 cm = 0.08 m
- Width = 5 cm = 0.05 m
- Height = 4 cm = 0.04 m

Substituting the values into the formula:
\[
V = 0.08 \, \text{m} \times 0.05 \, \text{m} \times 0.04 \, \text{m} = 0.00016 \, \text{m}^3
\]

2. **Calculate the mass of the block:**
The mass \( m \) can be calculated using the density \( \rho \) with the formula:
\[
m = \rho \times V
\]

Given:
- Density of iron \( \rho = 7,874 \, \text{kg/m}^3\)

Now substituting the values:
\[
m = 7,874 \, \text{kg/m}^3 \times 0.00016 \, \text{m}^3 = 1.25984 \, \text{kg}
\]

3. **Convert kg to grams:**
Since 1 kg = 1000 g,
\[
m = 1.25984 \, \text{kg} \times 1000 \, \text{g/kg} = 1259.84 \, \text{g}
\]

Therefore, the correct mass of the iron block is:
**1,259.84 g**

So the correct response is:
**1,259.84 g**