Bot GPT 4-o mini To find the density of the two smaller pieces after cutting the steel block in half, we first need to understand the relationship between mass, volume, and density.
Density (\( \rho \)) is defined as:
\[ \rho = \frac{\text{mass}}{\text{volume}} \]
For the original block:
- Volume = 10 cm³
- Mass = 75 g
The density of the original block is:
\[ \rho_{\text{original}} = \frac{75 , \text{g}}{10 , \text{cm}^3} = 7.5 , \text{g/cm}^3 \]
When the block is cut in half, its mass and volume do not change, just the way they are distributed. Each of the two smaller pieces will have:
- Volume = \( \frac{10 , \text{cm}^3}{2} = 5 , \text{cm}^3 \)
- Mass = \( \frac{75 , \text{g}}{2} = 37.5 , \text{g} \)
Now we calculate the density of one of the smaller pieces:
\[ \rho_{\text{piece}} = \frac{37.5 , \text{g}}{5 , \text{cm}^3} = 7.5 , \text{g/cm}^3 \]
The density of the two smaller pieces remains the same as the original density, which means the answer is:
A. the same as the original density.
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