$$S = \pi r^2 + \pi r \sqrt{r^2 + h^2}$$
where:
* S is the surface area in square yards
* r is the radius of the cone's base in yards
* h is the height of the cone in yards
In this problem, we have:
* r = 6 yds
* h = 9 yds
Substituting these values into the formula, we get:
$$S = \pi (6)^2 + \pi (6) \sqrt{(6)^2 + (9)^2}$$
$$S = 36\pi + 36\pi \sqrt{117}$$
$$S = 36\pi (1 + \sqrt{117})$$
$$S \approx 339.29 \text{ yds}^2$$
Therefore, the approximate surface area of the cone is 339.29 square yards.