The volume a pyramid of base area `25 cm^(2)` and height 12 cm is :

Options

A. `200 cm^(3) `
B. `100 cm^(3) `
C. `400 cm^(3) `
D. `800 cm^(3)`

Answer

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

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

### Step-by-Step Solution:

1. **Identify the Base Area and Height**:
- Base Area (A) = 25 cm²
- Height (h) = 12 cm

2. **Substitute the Values into the Formula**:
\[ \text{Volume} = \frac{1}{3} \times 25 \, \text{cm}^2 \times 12 \, \text{cm} \]

3. **Calculate the Volume**:
- First, calculate the product of the base area and height:
\[ 25 \times 12 = 300 \, \text{cm}^3 \]
- Now, multiply by \(\frac{1}{3}\):
\[ \text{Volume} = \frac{1}{3} \times 300 = 100 \, \text{cm}^3 \]

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