To find the volume of a rectangular piece of iron, we use the formula for the volume of a rectangular prism:
[tex]\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \][/tex]
Given the dimensions of the rectangular piece of iron:
- Length [tex]\( \text{length} = 7.08 \times 10^{-3} \)[/tex] meters
- Width [tex]\( \text{width} = 2.18 \times 10^{-2} \)[/tex] meters
- Height [tex]\( \text{height} = 4.51 \times 10^{-3} \)[/tex] meters
Let's substitute these values into the formula:
[tex]\[ \text{Volume} = (7.08 \times 10^{-3}) \times (2.18 \times 10^{-2}) \times (4.51 \times 10^{-3}) \][/tex]
Carrying out this multiplication, we get:
[tex]\[ \text{Volume} = 6.9609144 \times 10^{-7} \][/tex]
After rounding this to the required significant figures as given in the answer choices, it matches:
[tex]\[ \text{Volume} \approx 6.96 \times 10^{-7} \, \text{m}^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ 6.96 \times 10^{-7} \, \text{m}^3 \][/tex]
