To find the surface area of a cone, we can use the following formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where \( r \) is the radius and \( l \) is the slant height (hypotenuse).
From the information provided:
- The radius \( r = 6 \)
- The slant height \( l = 11 \)
Now substitute these values into the formula:
\[ \text{Surface Area} = \pi \times 6 \times (6 + 11) \] \[ = \pi \times 6 \times 17 \] \[ = \pi \times 102 \]
Now substitute \( \pi \) with \( 3.14 \):
\[ \text{Surface Area} = 3.14 \times 102 \] \[ = 320.28 \]
Rounding to the nearest tenth:
\[ \text{Surface Area} \approx 320.3 \]
Thus, the surface area of the cone is approximately 320.3 square units.
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