The total surface area of a cube is `150cm^(2)`. Its volume is

Options

A. `216cm^(3)`
B. `125 cm^(3)`
C. `64cm^(3)`
D. `1000cm^(3)`

Answer

To find the volume of a cube when the total surface area is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Total Surface Area of a Cube**:
The total surface area (TSA) of a cube is given by the formula:
\[ \text{TSA} = 6a^2 \]
where \( a \) is the length of a side of the cube.

2. **Set Up the Equation**:
We know from the problem that the total surface area is \( 150 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 150 \]

3. **Solve for \( a^2 \)**:
To isolate \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{150}{6} \]
Simplifying the right side:
\[ a^2 = 25 \]

4. **Find the Value of \( a \)**:
To find \( a \), take the square root of both sides:
\[ a = \sqrt{25} = 5 \, \text{cm} \]

5. **Calculate the Volume of the Cube**:
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 5^3 = 5 \times 5 \times 5 \]
Calculating this:
\[ V = 25 \times 5 = 125 \, \text{cm}^3 \]

### Final Answer:
The volume of the cube is \( 125 \, \text{cm}^3 \).

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