To find the surface area of a cone, we use the following formula:
\(\[ \text{Surface Area} = \pi r (r + l) \]\)
where:
- \(\( r \)\) is the radius of the cone
- \(\( l \)\) is the slant height of the cone
Given:
- \(\( r = 11 \)\) feet
- \(\( l = 15 \)\) feet
Let's calculate the surface area step-by-step:
1. Substitute the given values into the formula:
\(\[
\text{Surface Area} = \pi \times 11 \times (11 + 15)
\]\)
2. Add the numbers inside the parentheses:
\(\[
11 + 15 = 26
\]\)
So now the formula becomes:
\(\[
\text{Surface Area} = \pi \times 11 \times 26
\]\)
3. Multiply the radius \(\( r \)\) by the result in the parentheses:
\(\[
11 \times 26 = 286
\]\)
So the formula now is:
\(\[
\text{Surface Area} = \pi \times 286
\]\)
4. Multiply by \(\( \pi \)\) (using the approximate value \(\( \pi \approx 3.141592653589793 \)\)):
\(\[
\text{Surface Area} \approx 3.141592653589793 \times 286
\]\)
\(\[
\text{Surface Area} \approx 898.059
\]\)
5. Round the result to the nearest tenth:
\(\[
\text{Surface Area} \approx 898.1 \text{ square feet}
\]\)
Thus, the surface area of the cone is approximately \(\( 898.1 \)\) square feet when rounded to the nearest tenth.
