To find the surface area of a cone, you can use the formula:
\[ \text{Surface Area} = \pi r l + \pi r^2 \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone,
- \( \pi \) is approximately 3.14.
First, we need to find the radius of the cone. The diameter is given as 14 inches, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ inches} \]
Next, we can substitute the values of \( r \) and \( l \) into the surface area formula. The slant height \( l \) is given as 20 inches.
Now we can calculate the surface area:
- Calculate the lateral (side) surface area:
\[ \pi r l = 3.14 \times 7 \times 20 = 3.14 \times 140 = 439.6 \text{ square inches} \]
- Calculate the base surface area:
\[ \pi r^2 = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \text{ square inches} \]
- Add both areas together to get the total surface area:
\[ \text{Surface Area} = 439.6 + 153.86 = 593.46 \text{ square inches} \]
Therefore, the surface area of the cone peak is approximately:
\[ \boxed{593.46} \text{ square inches} \]
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