What is the volume of a cube whose surface area is `150 cm ^(2)` (meter square) ?
(a)1125 cubic metres
(b)225 cubic metres
(c)125 cubic metres
(d)None of the above

Options

A. 1125 cubic metres
B. 225 cubic metres
C. 125 cubic metres
D. None of the above

Answer

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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