Answer :
To find the volume of a cube, you use the formula:
[tex]\[ \text{Volume} = \text{side length}^3 \][/tex]
In this case, the side length of the cube is [tex]\( 1.2 \times 10^{-2} \, \text{meters} \)[/tex].
Step-by-step solution:
1. Determine the side length of the cube:
[tex]\[ \text{Side length} = 1.2 \times 10^{-2} \, \text{m} \][/tex]
2. Calculate the volume:
[tex]\[ \text{Volume} = (1.2 \times 10^{-2} \, \text{m})^3 \][/tex]
3. Expand the calculation:
[tex]\[ \begin{align*} (1.2 \times 10^{-2} \, \text{m})^3 & = 1.2^3 \times (10^{-2})^3 \\ & = 1.728 \times 10^{-6} \, \text{m}^3 \end{align*} \][/tex]
So, the volume of the cube is:
[tex]\[ 1.728 \times 10^{-6} \, \text{m}^3 \][/tex]
Among the answer choices provided:
1. [tex]\(1.7 \times 10^{-6} \, \text{m}^3\)[/tex]
2. [tex]\(1.73 \times 10^{-6} \, \text{m}^3\)[/tex]
3. [tex]\(1.70 \times 10^{-6} \, \text{m}^3\)[/tex]
4. [tex]\(1.732 \times 10^{-6} \, \text{m}^3\)[/tex]
None are exactly 1.728, but the closest approximation provided is:
[tex]\[ (2) \, 1.73 \times 10^{-6} \, \text{m}^3 \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{1.73 \times 10^{-6} \, \text{m}^3} \][/tex]
[tex]\[ \text{Volume} = \text{side length}^3 \][/tex]
In this case, the side length of the cube is [tex]\( 1.2 \times 10^{-2} \, \text{meters} \)[/tex].
Step-by-step solution:
1. Determine the side length of the cube:
[tex]\[ \text{Side length} = 1.2 \times 10^{-2} \, \text{m} \][/tex]
2. Calculate the volume:
[tex]\[ \text{Volume} = (1.2 \times 10^{-2} \, \text{m})^3 \][/tex]
3. Expand the calculation:
[tex]\[ \begin{align*} (1.2 \times 10^{-2} \, \text{m})^3 & = 1.2^3 \times (10^{-2})^3 \\ & = 1.728 \times 10^{-6} \, \text{m}^3 \end{align*} \][/tex]
So, the volume of the cube is:
[tex]\[ 1.728 \times 10^{-6} \, \text{m}^3 \][/tex]
Among the answer choices provided:
1. [tex]\(1.7 \times 10^{-6} \, \text{m}^3\)[/tex]
2. [tex]\(1.73 \times 10^{-6} \, \text{m}^3\)[/tex]
3. [tex]\(1.70 \times 10^{-6} \, \text{m}^3\)[/tex]
4. [tex]\(1.732 \times 10^{-6} \, \text{m}^3\)[/tex]
None are exactly 1.728, but the closest approximation provided is:
[tex]\[ (2) \, 1.73 \times 10^{-6} \, \text{m}^3 \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{1.73 \times 10^{-6} \, \text{m}^3} \][/tex]
