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)

Question

Responses

8,113.76 square centimeters
8,113.76 square centimeters

2,923.34 square centimeters
2,923.34 square centimeters

1,789.8 square centimeters
1,789.8 square centimeters

3,579.6 square centimeters

Answer 1

The surface area \( A \) of a cone (the nón lá) can be calculated using the formula:

\[ A = \pi r l \]

where:

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

First, we need to find the radius \( r \) from the diameter: \[ r = \frac{\text{diameter}}{2} = \frac{38 , \text{cm}}{2} = 19 , \text{cm} \]

Now, we can plug in the values into the surface area formula. Using \( \pi = 3.14 \) and \( l = 30 , \text{cm} \):

\[ A = 3.14 \times 19 , \text{cm} \times 30 , \text{cm} \]

Calculating the components one step at a time:

1. Calculate \( 19 \times 30 \): \[ 19 \times 30 = 570 \]

2. Now multiply by \( \pi \): \[ A = 3.14 \times 570 \] \[ A = 1,791.8 , \text{square centimeters} \]

So the surface area of the nón lá is approximately 1,789.8 square centimeters.

Thus, the correct response is:

1,789.8 square centimeters.