To solve this problem, we need to find the mass of a rectangular prism based on its dimensions and density. Let's follow a step-by-step approach:
1. Convert the dimensions from inches to centimeters:
- Length [tex]\( L \)[/tex] = 9 inches
- Width [tex]\( W \)[/tex] = 3 inches
- Height [tex]\( H \)[/tex] = 2 inches
We know that 1 inch equals 2.54 centimeters.
[tex]\[
L = 9 \text{ inches} \times 2.54 \text{ cm/inch} = 22.86 \text{ cm}
\][/tex]
[tex]\[
W = 3 \text{ inches} \times 2.54 \text{ cm/inch} = 7.62 \text{ cm}
\][/tex]
[tex]\[
H = 2 \text{ inches} \times 2.54 \text{ cm/inch} = 5.08 \text{ cm}
\][/tex]
2. Calculate the volume of the rectangular prism in cubic centimeters:
The volume [tex]\( V \)[/tex] of a rectangular prism is given by the formula:
[tex]\[
V = L \times W \times H
\][/tex]
Substituting the converted dimensions:
[tex]\[
V = 22.86 \text{ cm} \times 7.62 \text{ cm} \times 5.08 \text{ cm} = 885.066672 \text{ cm}^3
\][/tex]
3. Using the density to find the mass:
The density [tex]\( \rho \)[/tex] is given as 12.1 grams per cubic centimeter [tex]\( \text{g/cm}^3 \)[/tex].
The mass [tex]\( M \)[/tex] can be calculated using the formula:
[tex]\[
M = V \times \rho
\][/tex]
Substituting the values:
[tex]\[
M = 885.066672 \text{ cm}^3 \times 12.1 \text{ g/cm}^3 = 10708.3067112 \text{ g}
\][/tex]
4. Rounding the mass to the nearest gram:
To the nearest gram:
[tex]\[
M \approx 10708 \text{ g}
\][/tex]
Therefore, the mass of the object is about 10708 grams.
