To find the volume of a square pyramid, we use the formula:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Given:
- The base length of the pyramid is [tex]\( \frac{1}{2} \, \text{ft} \)[/tex].
- The height of the pyramid is [tex]\( \frac{1}{4} \, \text{ft} \)[/tex].
### Step 1: Calculate the base area
The base of the pyramid is a square, so the area of the base (A) is given by:
[tex]\[ \text{Base Area} = \text{side}^2 \][/tex]
Here, the side length is [tex]\( \frac{1}{2} \, \text{ft} \)[/tex].
[tex]\[
\text{Base Area} = \left( \frac{1}{2} \right)^2 = \frac{1}{4} \, \text{ft}^2
\][/tex]
### Step 2: Calculate the volume of the pyramid
Using the formula for the volume of a square pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Substitute the base area and height:
[tex]\[ V = \frac{1}{3} \times \frac{1}{4} \, \text{ft}^2 \times \frac{1}{4} \, \text{ft} \][/tex]
[tex]\[
V = \frac{1}{3} \times \frac{1}{16} \, \text{ft}^3
\][/tex]
[tex]\[
V = \frac{1}{48} \, \text{ft}^3
\][/tex]
### Step 3: Simplify the Volume Expression
The simplified volume is:
[tex]\[ V = 0.020833333333333332 \, \text{ft}^3 \][/tex]
Therefore, the volume of the square pyramid is [tex]\(\boxed{0.020833333333333332 \, \text{ft}^3}\)[/tex].
