To find the surface area of a cone, we use the formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where \( r \) is the radius and \( l \) is the slant height.
In this case:
- \( r = 4 \) ft
- \( l = 10 \) ft
Now, substitute these values into the formula:
\[ \text{Surface Area} = \pi \times 4 \times (4 + 10) \] \[ = \pi \times 4 \times 14 \] \[ = \pi \times 56 \]
Now, calculate this using an approximate value for \(\pi \) (around 3.14):
\[ \text{Surface Area} \approx 3.14 \times 56 \approx 175.84 \]
Rounding to the nearest foot, the surface area of the cone is approximately:
\[ \text{Surface Area} \approx 176 \text{ ft}^2 \]
So, the surface area of the cone is 176 ft².