To find the surface area of a cone, we use the formula:
\[ A = \pi r^2 + \pi r l \]
where:
- \(A\) is the surface area,
- \(r\) is the radius of the base of the cone,
- \(l\) is the slant height.
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Calculate the radius:
- The diameter is 14 inches, so the radius \(r\) is: \[ r = \frac{14}{2} = 7 \text{ inches} \]
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Use the slant height:
- Given slant height \(l = 20\) inches.
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Substitute the values into the surface area formula: \[ A = \pi (7)^2 + \pi (7)(20) \]
First, calculate \( \pi (7)^2 \): \[ \pi (7^2) = \pi (49) \approx 153.94 \]
Now calculate \( \pi (7)(20) \): \[ \pi (7)(20) = \pi (140) \approx 439.82 \]
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Combine the areas: \[ A \approx 153.94 + 439.82 \approx 593.76 \]
Thus, the surface area of the cone, to the nearest hundredth, is:
\[ \boxed{593.76} \text{ square inches} \]
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