Question

Question A nón lá is a traditional Vietnamese hat in the shape of a perfect cone. What is the surface area of a hat with a diameter of 38 cm and a slant height of 30 cm? Use 3.14 for pi.(1 point) Responses 8,113.76 square centimeters 8,113.76 square centimeters - no response given 3,579.6 square centimeters 3,579.6 square centimeters - no response given 1,789.8 square centimeters 1,789.8 square centimeters - no response given 2,923.34 square centimeters

Answer 1

To find the surface area of a conical hat, we can 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,
- \( l \) is the slant height of the cone.

Given:
- The diameter of the hat is 38 cm, thus the radius \( r \) is half of that:

\[
r = \frac{38}{2} = 19 \text{ cm}
\]

- The slant height \( l \) is 30 cm.

Substituting these values into the formula:

\[
\text{Lateral Surface Area} = 3.14 \times 19 \times 30
\]

Now calculate it step by step:

1. Calculate \( 19 \times 30 \):

\[
19 \times 30 = 570
\]

2. Now multiply by \( \pi \) (which we've approximated as 3.14):

\[
\text{Lateral Surface Area} = 3.14 \times 570 = 1,791.80 \text{ square centimeters}
\]

Thus, the surface area of the nón lá is approximately \( 1,791.80 \) square centimeters.

Since the provided options do not exactly match this calculated area, the closest approximate number is **1,789.8 square centimeters**.

Therefore, the correct answer is:

**1,789.8 square centimeters**.