To find the surface area of a cone, we need to calculate the lateral surface area and the base area. The formula for the surface area \( S \) of a cone is given by:
\[ S = \pi r l + \pi r^2 \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height (hypotenuse).
Given:
- Radius \( r = 6 \)
- Slant height \( l = 11 \)
Now, we can calculate the surface area as follows:
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 11 \]
Calculating this:
\[ = 3.14 \times 6 = 18.84 \] \[ 18.84 \times 11 = 207.24 \]
- Calculate the base area:
\[ \text{Base Area} = \pi r^2 = 3.14 \times 6^2 = 3.14 \times 36 \]
Calculating this:
\[ = 3.14 \times 36 = 113.04 \]
- Now, combine both areas to find the total surface area:
\[ S = 207.24 + 113.04 = 320.28 \]
Finally, rounding to the nearest tenth:
\[ S \approx 320.3 \]
Therefore, the surface area of the cone is 320.3 square units.