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

Answer 1

To calculate the mass of the iron block, we can follow these steps:

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

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

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

2. **Calculate the mass using density**:
The mass \( m \) can be calculated using the formula:
\[
m = \text{density} \times \text{volume}
\]
Given that the density of iron is \( 7,874 \, \text{kg/m}^3 \):
\[
m = 7,874 \, \text{kg/m}^3 \times 0.00016 \, \text{m}^3 = 1.25984 \, \text{kg}
\]

3. **Convert the mass to grams**:
Since \( 1 \, \text{kg} = 1,000 \, \text{g} \):
\[
m = 1.25984 \, \text{kg} \times 1,000 = 1,259.84 \, \text{g}
\]

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

The correct response is **1,259.84 g**.