Question

Determine the surface area of
a cone if the diameter of the
base is 14 ft., and the slant
height of the cone is 19 ft.
Use and round your
answer to the nearest
hundredth. (1 point)
π = 3.14

Answer 1

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

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

where \( r \) is the radius of the base, and \( l \) is the slant height.

1. **Find the radius**:
Given the diameter of the base is 14 ft, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{14 \, \text{ft}}{2} = 7 \, \text{ft}
\]

2. **Use the slant height**:
The slant height \( l \) is given as 19 ft.

3. **Plug values into the formula**:

\[
\text{Surface Area} = \pi r (r + l) = \pi (7 \, \text{ft}) (7 \, \text{ft} + 19 \, \text{ft})
\]

First, calculate \( r + l \):

\[
r + l = 7 \, \text{ft} + 19 \, \text{ft} = 26 \, \text{ft}
\]

Now, substituting back into the surface area formula:

\[
\text{Surface Area} = \pi (7 \, \text{ft}) (26 \, \text{ft})
\]

\[
\text{Surface Area} = 3.14 \times 7 \times 26
\]

Calculate \( 7 \times 26 \):

\[
7 \times 26 = 182
\]

Now multiply by \( \pi \):

\[
\text{Surface Area} = 3.14 \times 182
\]

Performing the multiplication:

\[
3.14 \times 182 = 572.28
\]

4. **Round to the nearest hundredth**:

The final surface area of the cone is:

\[
\boxed{572.28} \, \text{ft}^2
\]