Question

What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
(radius 6) ( hight 11)

Answer 1

sorry lenght is 11

Answer 2

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

\[
\text{Surface Area} = \pi r^2 + \pi r l
\]

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

First, we need to calculate the slant height \( l \) using the Pythagorean theorem:

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

Substituting the given values \( r = 6 \) and \( h = 11 \):

\[
l = \sqrt{6^2 + 11^2} = \sqrt{36 + 121} = \sqrt{157}
\]

Now, calculating \( \sqrt{157} \):

\[
\sqrt{157} \approx 12.53
\]

Now that we have \( l \), we can calculate the surface area:

\[
\text{Surface Area} = \pi r^2 + \pi r l
\]

Substituting the values:

\[
\text{Surface Area} = \pi (6^2) + \pi (6)(12.53)
\]

Calculating \( \pi (6^2) \):

\[
\pi (6^2) = \pi (36) \approx 3.14 \times 36 \approx 113.04
\]

Now calculating \( \pi (6)(12.53) \):

\[
\pi (6)(12.53) \approx 3.14 \times 6 \times 12.53 \approx 3.14 \times 75.18 \approx 236.60
\]

Now, adding both parts together:

\[
\text{Surface Area} \approx 113.04 + 236.60 \approx 349.64
\]

Finally, rounding to the nearest tenth:

\[
\text{Surface Area} \approx 349.6
\]

Thus, the surface area of the cone is approximately **349.6 square units**.

Answer 3

No problem! Let's recalculate the surface area of the cone with the correct height of 11 units. The radius remains 6 units.

The formula for the surface area of a cone is:

\[
\text{Surface Area} = \pi r^2 + \pi r l
\]

where:
- \( r \) = radius of the base of the cone,
- \( h \) = height of the cone,
- \( l \) = slant height of the cone, calculated using:

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

### Given:
- \( r = 6 \)
- \( h = 11 \)

### Step 1: Calculate the Slant Height \( l \)

\[
l = \sqrt{r^2 + h^2} = \sqrt{6^2 + 11^2} = \sqrt{36 + 121} = \sqrt{157}
\]

Calculating \( \sqrt{157} \):

\[
\sqrt{157} \approx 12.53
\]

### Step 2: Calculate the Surface Area

Now we can substitute back into the surface area formula:

\[
\text{Surface Area} = \pi r^2 + \pi r l
\]

Calculating \( \pi r^2 \) first:

\[
\pi r^2 = \pi (6^2) = \pi (36) \approx 3.14 \times 36 \approx 113.04
\]

Next, calculate \( \pi r l \):

\[
\pi r l = \pi (6)(12.53) \approx 3.14 \times 6 \times 12.53 \approx 3.14 \times 75.18 \approx 236.60
\]

### Step 3: Add Both Parts Together

Now, we can add these two components together:

\[
\text{Surface Area} \approx 113.04 + 236.60 \approx 349.64
\]

### Final Step: Round to the Nearest Tenth

Rounding gives us:

\[
\text{Surface Area} \approx 349.6
\]

Thus, the surface area of the cone with a radius of 6 and a height of 11 is approximately **349.6 square units**.