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Answer :
To solve this problem, we need to find the volume of a cube with an edge length of 1.5 feet, and then convert that volume into cubic meters.
### Step-by-Step Solution:
1. Understand the given data:
- The edge length of the cube is 1.5 feet.
- The conversion factor from meters to feet is given as [tex]\(1 \, \text{m} = 3.281 \, \text{ft}\)[/tex].
2. Convert the edge length from feet to meters:
- To do this, we use the conversion factor:
[tex]\[
\text{edge}_{\text{m}} = \text{edge}_{\text{ft}} \times \left(\frac{1 \, \text{m}}{3.281 \, \text{ft}}\right)
\][/tex]
- Substituting the edge length:
[tex]\[
\text{edge}_{\text{m}} = 1.5 \, \text{ft} \times \left(\frac{1 \, \text{m}}{3.281 \, \text{ft}}\right) \approx 0.457 \, \text{m}
\][/tex]
3. Calculate the volume of the cube in cubic meters:
- The formula to find the volume of a cube is given by [tex]\(V = \text{edge}^3\)[/tex].
- So, we calculate:
[tex]\[
V_{\text{m}^3} = (0.457 \, \text{m})^3 \approx 0.0956 \, \text{m}^3
\][/tex]
4. Compare the calculated volume with the given choices:
- The options provided are:
[tex]\[
\begin{array}{ll}
9.5 \times 10^{-2} \, \text{m}^3 & (0.095) \\
10.5 \, \text{m}^3 & \\
9.6 \times 10^{-2} \, \text{m}^3 & (0.096) \\
0.21 \, \text{m}^3 & \\
1.2 \times 10^2 \, \text{m}^3 & (120)
\end{array}
\][/tex]
- The closest value to our calculation of [tex]\(0.0956 \, \text{m}^3\)[/tex] is [tex]\(9.6 \times 10^{-2} \, \text{m}^3\)[/tex].
### Conclusion:
The volume of a cube with an edge of 1.5 feet, when converted to cubic meters, is approximately [tex]\(9.6 \times 10^{-2} \, \text{m}^3\)[/tex]. So, the correct option is:
[tex]\[
\boxed{9.6 \times 10^{-2} \, \text{m}^3}
\][/tex]
### Step-by-Step Solution:
1. Understand the given data:
- The edge length of the cube is 1.5 feet.
- The conversion factor from meters to feet is given as [tex]\(1 \, \text{m} = 3.281 \, \text{ft}\)[/tex].
2. Convert the edge length from feet to meters:
- To do this, we use the conversion factor:
[tex]\[
\text{edge}_{\text{m}} = \text{edge}_{\text{ft}} \times \left(\frac{1 \, \text{m}}{3.281 \, \text{ft}}\right)
\][/tex]
- Substituting the edge length:
[tex]\[
\text{edge}_{\text{m}} = 1.5 \, \text{ft} \times \left(\frac{1 \, \text{m}}{3.281 \, \text{ft}}\right) \approx 0.457 \, \text{m}
\][/tex]
3. Calculate the volume of the cube in cubic meters:
- The formula to find the volume of a cube is given by [tex]\(V = \text{edge}^3\)[/tex].
- So, we calculate:
[tex]\[
V_{\text{m}^3} = (0.457 \, \text{m})^3 \approx 0.0956 \, \text{m}^3
\][/tex]
4. Compare the calculated volume with the given choices:
- The options provided are:
[tex]\[
\begin{array}{ll}
9.5 \times 10^{-2} \, \text{m}^3 & (0.095) \\
10.5 \, \text{m}^3 & \\
9.6 \times 10^{-2} \, \text{m}^3 & (0.096) \\
0.21 \, \text{m}^3 & \\
1.2 \times 10^2 \, \text{m}^3 & (120)
\end{array}
\][/tex]
- The closest value to our calculation of [tex]\(0.0956 \, \text{m}^3\)[/tex] is [tex]\(9.6 \times 10^{-2} \, \text{m}^3\)[/tex].
### Conclusion:
The volume of a cube with an edge of 1.5 feet, when converted to cubic meters, is approximately [tex]\(9.6 \times 10^{-2} \, \text{m}^3\)[/tex]. So, the correct option is:
[tex]\[
\boxed{9.6 \times 10^{-2} \, \text{m}^3}
\][/tex]
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