To calculate the surface area of a cone, we use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height (hypotenuse), and
- \( \pi \) is approximately 3.14.
Given:
- Radius, \( r = 6 \)
- Slant height, \( l = 11 \)
Now we can calculate each component:
-
Calculate the area of the base: \[ \pi r^2 = 3.14 \times (6^2) = 3.14 \times 36 = 113.04 \]
-
Calculate the lateral surface area: \[ \pi r l = 3.14 \times 6 \times 11 = 3.14 \times 66 = 207.24 \]
-
Add both areas together to get the total surface area: \[ \text{Surface Area} = 113.04 + 207.24 = 320.28 \]
-
Rounding to the nearest tenth: \[ \text{Surface Area} \approx 320.3 \text{ square units} \]
Thus, the surface area of the cone is 320.3 square units.