To find the surface area of the cone peak, we need to calculate the lateral surface area and the base area of the cone. However, since you mentioned it as a "peak," we will focus mainly on the lateral surface area, as the base of the peak is typically not included.
The formula for the lateral surface area \( A \) of a cone is given by:
\[ A = \pi r l \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
Given:
- The diameter of the cone is 14 inches, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{14}{2} = 7 \text{ inches} \]
- The slant height \( l \) is given as 20 inches.
Now we can substitute the values into the formula:
\[ A = \pi \times 7 \times 20 \]
\[ A = 140\pi \]
Now, if you want a numerical answer, we can approximate \( \pi \) as 3.14:
\[ A \approx 140 \times 3.14 \approx 439.6 \text{ square inches} \]
Thus, the lateral surface area of the cone peak is approximately \( 439.6 \) square inches. If you want to keep it in terms of \( \pi \), it would be \( 140\pi \) square inches.
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