Question

Surface Area of Cones Practice
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Question
What is the surface area, in square centimeters, of a cone with a diameter of 12 feet and a slant height of 14 feet? Use 3.14 for pi and round to the nearest tenth, if necessary.

Answer 1

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

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

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

### Step 1: Find the radius
The diameter of the cone is 12 feet, so the radius \( r \) is half of the diameter:

\[
r = \frac{12}{2} = 6 \text{ feet}
\]

### Step 2: Plug in the values into the formula
Given \( r = 6 \) feet and \( l = 14 \) feet, we can calculate the surface area:

1. **Calculate the base area:**
\[
\pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ square feet}
\]

2. **Calculate the lateral surface area:**
\[
\pi r l = 3.14 \times 6 \times 14
\]
First, calculate \( 6 \times 14 \):
\[
6 \times 14 = 84
\]
Now calculate the lateral surface area:
\[
\pi r l = 3.14 \times 84 = 263.76 \text{ square feet}
\]

### Step 3: Add both areas
Now, add the base area and the lateral surface area to find the total surface area:

\[
\text{Surface Area} = 113.04 + 263.76 = 376.8 \text{ square feet}
\]

### Final Answer
Thus, the surface area of the cone is approximately **376.8 square feet**.