Calculate the surface area of a cone whose radius is 6cm and the heights is 8cm

The radius ($r$) is 6 cm and the height ($h$) is 8 cm. The slant height can be found using the Pythagorean theorem:

$$l = \sqrt{r^2 + h^2}$$ $$l = \sqrt{6^2 + 8^2}$$ $$l = \sqrt{36 + 64}$$ $$l = \sqrt{100}$$ $$l = 10 \text{ cm}$$

The formula for the surface area of a cone is the sum of the area of the base ($\pi r^2$) and the lateral surface area ($\pi r l$):

$$A = \pi r^2 + \pi r l$$

Substitute the values $r = 6$ cm and $l = 10$ cm into the formula:

$$A = \pi (6)^2 + \pi (6)(10)$$ $$A = 36\pi + 60\pi$$ $$A = 96\pi \text{ cm}^2$$

The surface area of the cone is $\text{96}\pi \text{ cm}^2$.