To find the volume of a cube given its surface area, we can follow these steps:
### Step 1: Understand the formulas
The surface area \( S \) of a cube is given by the formula:
\[ S = 6a^2 \]
where \( a \) is the length of one side of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
### Step 2: Set up the equation
We are given that the surface area \( S \) is \( 150 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 150 \]
### Step 3: Solve for \( a^2 \)
To find \( a^2 \), we divide both sides of the equation by 6:
\[ a^2 = \frac{150}{6} \]
\[ a^2 = 25 \]
### Step 4: Solve for \( a \)
Now, we take the square root of both sides to find \( a \):
\[ a = \sqrt{25} \]
\[ a = 5 \, \text{cm} \]
### Step 5: Calculate the volume
Now that we have \( a \), we can find the volume \( V \) of the cube:
\[ V = a^3 = 5^3 \]
\[ V = 125 \, \text{cm}^3 \]
### Step 6: Convert to cubic meters
Since the options are in cubic meters, we need to convert \( 125 \, \text{cm}^3 \) to cubic meters. We know that:
\[ 1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3 \]
Thus,
\[ V = \frac{125}{1,000,000} \, \text{m}^3 = 0.000125 \, \text{m}^3 \]
### Conclusion
Since \( 0.000125 \, \text{m}^3 \) is not listed in the options, the answer is:
(d) None of the above.
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