The whole surface of a cube is 150 sq. cm. Then the volume of the cube is

Options

A. `125 cm^(3)`
B. `216 cm^(3)`
C. `343 cm^(3)`
D. `512 cm^(3)`

Answer

To find the volume of the cube given its surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the surface area of a cube**:
The surface area (SA) of a cube is given by the formula:
\[ SA = 6a^2 \]
where \( a \) is the length of one side of the cube.

2. **Set up the equation with the given surface area**:
We know the surface area is 150 sq. cm. Therefore, we can write:
\[ 6a^2 = 150 \]

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

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

5. **Calculate the volume of the cube**:
The volume (V) of a cube is given by the formula:
\[ V = a^3 \]
Substitute \( a = 5 \) cm into the formula:
\[ V = 5^3 = 125 \text{ cubic cm} \]

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

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