Question

A non la 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

Answer 1

To calculate the surface area of a conical hat (or a cone), we can use the formula for the lateral surface area of a cone, which is given by:

\[
A = \pi r l
\]

where:
- \(A\) is the lateral surface area,
- \(r\) 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, so the radius \(r\) can be calculated as:

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

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

Now, we can substitute these values into the formula:

\[
A = \pi r l = 3.14 \times 19 \text{ cm} \times 30 \text{ cm}
\]

Calculating it step by step:

1. First, calculate \(19 \times 30\):

\[
19 \times 30 = 570
\]

2. Now, substitute this back into the formula:

\[
A = 3.14 \times 570
\]

3. Now calculate \(3.14 \times 570\):

\[
3.14 \times 570 = 1798.0 \text{ cm}^2
\]

Thus, the lateral surface area of the non la (Vietnamese hat) is approximately:

\[
\boxed{1798.0 \text{ cm}^2}
\]