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

49.2125 g
49.2125 g

1,259.84 g
1,259.84 g

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

0.49 g

Answer 1

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

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

1. **Calculate the volume of the block:**

The volume \( V \) of a rectangular block is calculated using the formula:

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

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

Now calculate the volume:

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

2. **Calculate the mass using density:**

Given the density of iron is:

\[
\text{Density} = 7,874 \, \text{kg/m}^3
\]

Now substitute in the values to find the mass:

\[
\text{Mass} = 7,874 \, \text{kg/m}^3 \times 0.00016 \, \text{m}^3
\]
\[
\text{Mass} = 1.25984 \, \text{kg}
\]

3. **Convert kilograms to grams:**

Since 1 kg = 1000 g:

\[
\text{Mass} = 1.25984 \, \text{kg} \times 1000 \, \text{g/kg} = 1259.84 \, \text{g}
\]

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

From your options, the correct response is:

**1,259.84 g**.