Question

Find the surface area of the cone. Give your final answer rounded to the nearest whole number. Use 3.14 for pi.
radius is 11 in. height is 14 in.

Answer 1

To find the surface area of a cone, you can use the formula:

\[
\text{Surface Area} = \pi r (r + l)
\]

where:
- \( r \) is the radius,
- \( l \) is the slant height of the cone.

First, we need to calculate the slant height \( l \) using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle where one leg is the height of the cone and the other leg is the radius.

The formula for the slant height is:

\[
l = \sqrt{r^2 + h^2}
\]

Given:
- \( r = 11 \) in
- \( h = 14 \) in

Now calculating \( l \):

\[
l = \sqrt{11^2 + 14^2} = \sqrt{121 + 196} = \sqrt{317}
\]

Calculating \( \sqrt{317} \):

\[
l \approx 17.78 \text{ in (rounded to two decimal places)}
\]

Now we substitute \( r \) and \( l \) into the surface area formula:

\[
\text{Surface Area} = \pi r (r + l)
\]
\[
= 3.14 \times 11 \times (11 + 17.78)
\]
\[
= 3.14 \times 11 \times 28.78
\]
\[
= 3.14 \times 11 \times 28.78 \approx 3.14 \times 316.58 \approx 995.43
\]

Now, rounding to the nearest whole number, the surface area of the cone is:

\[
\text{Surface Area} \approx 995 \text{ square inches}
\]

Thus, the final answer is:

\[
\boxed{995}
\]