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

1,789.8 square centimeters
1,789.8 square centimeters

3,579.6 square centimeters
3,579.6 square centimeters

8,113.76 square centimeters
8,113.76 square centimeters

2,923.34 square centimeters
2,923.34 square centimeters
Remaining Attempts : 3
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Answer 1

To find the surface area of a cone, you can use the formula:

\[ \text{Surface Area} = \pi r (r + l) \]

where:

• \( r \) is the radius of the base,
• \( l \) is the slant height,
• and \( \pi \) is approximately 3.14.

Given:

• The diameter is 38 cm, so the radius \( r \) is half of that: \[ r = \frac{38}{2} = 19 \text{ cm} \]
• The slant height \( l \) is 30 cm.

Now, plug the values into the surface area formula:

\[ \text{Surface Area} = 3.14 \times 19 \times (19 + 30) \] \[ = 3.14 \times 19 \times 49 \] Calculating \( 19 + 30 = 49 \):

Now calculate \( 19 \times 49 \): \[ 19 \times 49 = 931 \]

Now calculate the surface area: \[ \text{Surface Area} = 3.14 \times 931 = 2,922.74 \text{ square centimeters} \]

When rounded, that is approximately 2,923.34 square centimeters.

Thus, the correct response is: 2,923.34 square centimeters.