Cones, Cylinders, & Spheres Online Practice

Question

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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

2,923.34 square centimeters
2,923.34 square centimeters - incorrect

8,113.76 square centimeters
8,113.76 square centimeters - no response given

1,789.8 square centimeters
1,789.8 square centimeters - no response given

3,579.6 square centimeters
3,579.6 square centimeters - no response given
Remaining Attempts : 2
Incorrect

The bottom of the hat is open.

Answer 1

To find the surface area of a cone with an open bottom, we need to use the formula for the lateral surface area of a cone and the area of the base. However, since the bottom of the nón lá hat is open, we only need the lateral surface area.

The formula for the lateral surface area \(A\) of a cone is:

\[ A = \pi r l \]

where:

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

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

Now we can plug in the values for \(r\) and \(l\) into the formula:

• \(l = 30\) cm,
• \(r = 19\) cm,
• \(\pi \approx 3.14\).

Thus, the lateral surface area is: \[ A = 3.14 \times 19 \text{ cm} \times 30 \text{ cm} \]

Now, let's calculate it: \[ A = 3.14 \times 19 \times 30 = 3.14 \times 570 = 1,789.8 \text{ square centimeters} \]

Therefore, the surface area of the nón lá hat is 1,789.8 square centimeters.