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