Question

Surface Area of Cones Practice
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Question
A cook wants to cover the side of a cone-shaped funnel with parchment paper to avoid any leaks or spills. The funnel has a diameter of 6 inches and a slant height of 4 inches. How many square inches of parchment paper is needed to cover the side of the funnel? Use 3.14 for pi and round your answer to the nearest hundredth.

Answer 1

To find the surface area of the side of a cone (the lateral surface area), we can use the formula:

\[
\text{Lateral Surface Area} = \pi r l
\]

where \( r \) is the radius of the base of the cone, and \( l \) is the slant height of the cone.

1. First, we need to determine the radius. The diameter of the funnel is given as 6 inches, so the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{6 \text{ inches}}{2} = 3 \text{ inches}
\]

2. The slant height \( l \) is already given as 4 inches.

3. Now, we can substitute \( r \) and \( l \) into the formula:

\[
\text{Lateral Surface Area} = 3.14 \times 3 \text{ inches} \times 4 \text{ inches}
\]

Now perform the multiplication:

\[
\text{Lateral Surface Area} = 3.14 \times 3 \times 4
\]

Calculating step-by-step:

\[
3.14 \times 3 = 9.42
\]

Then:

\[
9.42 \times 4 = 37.68
\]

Therefore, the lateral surface area (the amount of parchment paper needed to cover the side of the funnel) is:

\[
\boxed{37.68} \text{ square inches}
\]