Question

A cone shows a radius of 6 and hypotenuse or side as 11.
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.

(1 point)

Answer 1

To find the surface area of a cone, we need to calculate the lateral surface area and the base area. The formula for the surface area \( S \) of a cone is given by:

\[
S = \pi r l + \pi r^2
\]

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

Given:
- Radius \( r = 6 \)
- Slant height \( l = 11 \)

Now, we can calculate the surface area as follows:

1. Calculate the lateral surface area:

\[
\text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 11
\]

Calculating this:

\[
= 3.14 \times 6 = 18.84
\]
\[
18.84 \times 11 = 207.24
\]

2. Calculate the base area:

\[
\text{Base Area} = \pi r^2 = 3.14 \times 6^2 = 3.14 \times 36
\]

Calculating this:

\[
= 3.14 \times 36 = 113.04
\]

3. Now, combine both areas to find the total surface area:

\[
S = 207.24 + 113.04 = 320.28
\]

Finally, rounding to the nearest tenth:

\[
S \approx 320.3
\]

Therefore, the surface area of the cone is **320.3** square units.