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

1 answer

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.