The base of pyramid is a square whose side is 5 cm . It's vertical height is 12 cm . Volume of pyramid is

Options

A. `380 cm ^(3)`
B. `360 cm ^(3)`
C. `400 cm ^(3)`
D. none of these

Answer

To find the volume of a pyramid with a square base, we can use the formula:

\[ \text{Volume} = \frac{1}{3} \times \text{Area of Base} \times \text{Height} \]

### Step-by-step Solution:

1. **Identify the dimensions of the pyramid:**
- The side length of the square base is given as \(5 \, \text{cm}\).
- The vertical height of the pyramid is given as \(12 \, \text{cm}\).

2. **Calculate the area of the base:**
- Since the base is a square, the area \(A\) can be calculated using the formula:
\[ A = \text{side}^2 \]
- Substituting the side length:
\[ A = 5^2 = 25 \, \text{cm}^2 \]

3. **Substitute the area and height into the volume formula:**
- Now, substitute the area of the base and the height into the volume formula:
\[ \text{Volume} = \frac{1}{3} \times 25 \times 12 \]

4. **Calculate the volume:**
- First, calculate \(25 \times 12\):
\[ 25 \times 12 = 300 \]
- Now substitute this back into the volume formula:
\[ \text{Volume} = \frac{1}{3} \times 300 = 100 \, \text{cm}^3 \]

5. **Final answer:**
- The volume of the pyramid is \(100 \, \text{cm}^3\).