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)

square units

Answer 1

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

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

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

Given:
- Radius \( r = 6 \)
- Slant height \( l = 11 \)
- Use \( \pi = 3.14 \)

Now, we can plug in the values into the formula:

1. Calculate \( r + l \):
\[
r + l = 6 + 11 = 17
\]

2. Then calculate the surface area:
\[
\text{Surface Area} = \pi r (r + l) = 3.14 \times 6 \times 17
\]

3. Calculate \( 6 \times 17 \):
\[
6 \times 17 = 102
\]

4. Now multiply by \( \pi \):
\[
\text{Surface Area} = 3.14 \times 102 = 320.28
\]

Finally, round 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**.