Question

Find the surface area of the cone. The diameter is 16, and the slant height is 9. Use 3.14 for pi.

Answer 1

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

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

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

First, we need to find the radius from the diameter. The diameter is given as 16, so:

\[
r = \frac{\text{diameter}}{2} = \frac{16}{2} = 8
\]

Next, we know the slant height \( l \) is given as 9.

Now we can calculate the two areas:

1. **Lateral Surface Area**:
\[
\text{Lateral Surface Area} = \pi r l = 3.14 \times 8 \times 9
\]

Calculating this step-by-step:

\[
8 \times 9 = 72
\]
\[
3.14 \times 72 = 226.08
\]

Thus, the lateral surface area is \( 226.08 \).

2. **Base Area**:
\[
\text{Base Area} = \pi r^2 = 3.14 \times (8^2)
\]

Calculating \( 8^2 \):

\[
8^2 = 64
\]

Now multiplying:

\[
3.14 \times 64 = 200.96
\]

Thus, the base area is \( 200.96 \).

3. **Total Surface Area**:
Adding the lateral surface area and the base area together:

\[
A = \text{Lateral Surface Area} + \text{Base Area}
\]
\[
A = 226.08 + 200.96 = 427.04
\]

Therefore, the total surface area of the cone is:

\[
\boxed{427.04}
\]