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Answer :
To find the mass of the rectangular solid, we need to follow these steps:
1. Determine the volume of the rectangular solid:
The formula for the volume [tex]\( V \)[/tex] of a rectangular solid is:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given the dimensions:
[tex]\[
\text{length} = 8.00 \, \text{cm}, \quad \text{width} = 4.00 \, \text{cm}, \quad \text{height} = 2.00 \, \text{cm}
\][/tex]
Substituting these values into the formula:
[tex]\[
V = 8.00 \, \text{cm} \times 4.00 \, \text{cm} \times 2.00 \, \text{cm}
\][/tex]
[tex]\[
V = 64.0 \, \text{cm}^3
\][/tex]
2. Determine the mass of the solid:
The formula for mass [tex]\( m \)[/tex] is:
[tex]\[
m = \text{density} \times \text{volume}
\][/tex]
Given the density [tex]\( \rho \)[/tex] is:
[tex]\[
\rho = 10.0 \, \text{g/cm}^3
\][/tex]
Using the previously calculated volume:
[tex]\[
V = 64.0 \, \text{cm}^3
\][/tex]
Substituting these values into the formula for mass:
[tex]\[
m = 10.0 \, \text{g/cm}^3 \times 64.0 \, \text{cm}^3
\][/tex]
[tex]\[
m = 640.0 \, \text{g}
\][/tex]
Hence, the mass of the rectangular solid is 640 grams.
The correct answer is:
[tex]\[
\boxed{640 \, \text{grams}}
\][/tex]
1. Determine the volume of the rectangular solid:
The formula for the volume [tex]\( V \)[/tex] of a rectangular solid is:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given the dimensions:
[tex]\[
\text{length} = 8.00 \, \text{cm}, \quad \text{width} = 4.00 \, \text{cm}, \quad \text{height} = 2.00 \, \text{cm}
\][/tex]
Substituting these values into the formula:
[tex]\[
V = 8.00 \, \text{cm} \times 4.00 \, \text{cm} \times 2.00 \, \text{cm}
\][/tex]
[tex]\[
V = 64.0 \, \text{cm}^3
\][/tex]
2. Determine the mass of the solid:
The formula for mass [tex]\( m \)[/tex] is:
[tex]\[
m = \text{density} \times \text{volume}
\][/tex]
Given the density [tex]\( \rho \)[/tex] is:
[tex]\[
\rho = 10.0 \, \text{g/cm}^3
\][/tex]
Using the previously calculated volume:
[tex]\[
V = 64.0 \, \text{cm}^3
\][/tex]
Substituting these values into the formula for mass:
[tex]\[
m = 10.0 \, \text{g/cm}^3 \times 64.0 \, \text{cm}^3
\][/tex]
[tex]\[
m = 640.0 \, \text{g}
\][/tex]
Hence, the mass of the rectangular solid is 640 grams.
The correct answer is:
[tex]\[
\boxed{640 \, \text{grams}}
\][/tex]
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