To find the surface area of the side of the cone (also known as the lateral surface area), we use the formula for the lateral surface area of a cone:
\[ \text{Lateral Surface Area} = \pi r l \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
Given:
- \( r = 3 \) inches,
- \( l = 8 \) inches,
- \( \pi \approx 3.14 \).
Now, plug in the values into the formula:
\[ \text{Lateral Surface Area} = 3.14 \times 3 \times 8 \]
Calculating this step-by-step:
-
Calculate \( 3 \times 8 \): \[ 3 \times 8 = 24 \]
-
Now multiply by \( 3.14 \): \[ 3.14 \times 24 = 75.36 \]
Thus, the lateral surface area of the cone is:
\[ \text{Lateral Surface Area} \approx 75.36 \text{ square inches} \]
So the final answer, rounded to the nearest hundredth, is:
\[ \boxed{75.36} \] square inches.