To find the surface area of a cone, you can 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 of the cone.
Given:
- Diameter = 14 inches, so the radius \( r \) is half of the diameter: \[ r = \frac{14}{2} = 7 \text{ inches} \]
- Slant height \( l = 20 \text{ inches} \).
Now, substitute the values into the surface area formula:
\[ \text{Surface Area} = \pi \times 7 \times (7 + 20) \]
Calculating \( 7 + 20 \):
\[ 7 + 20 = 27 \]
Now substitute this back in:
\[ \text{Surface Area} = \pi \times 7 \times 27 \]
Calculating \( 7 \times 27 \):
\[ 7 \times 27 = 189 \]
Now substitute in:
\[ \text{Surface Area} = \pi \times 189 \]
Using \( \pi \approx 3.14159 \):
\[ \text{Surface Area} \approx 3.14159 \times 189 \approx 593.87351 \]
Rounding to the nearest hundredth:
\[ \text{Surface Area} \approx 593.87 \text{ square inches} \]
Thus, the surface area of the cone is approximately:
\[ \boxed{593.87} \text{ square inches} \]
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