To find the area of the side of a cone, we use the formula for the lateral surface area of a cone:
\[ \text{Lateral Surface Area} = \pi r l \]
where \( r \) is the radius of the base of the cone, and \( l \) is the slant height.
- Calculate the radius: Given that the diameter of the cone is 6 inches, the radius \( r \) is:
\[ r = \frac{\text{Diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
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Given the slant height: The slant height \( l \) is given as 4 inches.
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Now plug the values into the formula:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \cdot 3 \cdot 4 \]
- Calculate:
\[ \text{Lateral Surface Area} = 3.14 \cdot 3 = 9.42 \] \[ 9.42 \cdot 4 = 37.68 \]
Thus, the lateral surface area, or the amount of parchment paper needed to cover the side of the funnel, is approximately:
\[ \text{Lateral Surface Area} \approx 37.68 \text{ square inches} \]
Therefore, the answer, rounded to the nearest hundredth, is 37.68 square inches.