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

8,113.76 square centimeters
8,113.76 square centimeters

1,789.8 square centimeters
1,789.8 square centimeters

3,579.6 square centimeters

Answer 1

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

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

where:

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

Given:

• The diameter of the cone is 38 cm, so the radius \( r \) is \( \frac{38}{2} = 19 \) cm.
• The slant height \( l \) is 30 cm.

Now, we can plug these values into the formula:

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

Calculating \( 19 + 30 \):

\[ 19 + 30 = 49 \]

Now substituting this back into the surface area formula:

\[ \text{Surface Area} = 3.14 \times 19 \times 49 \]

Calculating \( 19 \times 49 \):

\[ 19 \times 49 = 931 \]

Now multiplying by \( \pi \):

\[ \text{Surface Area} = 3.14 \times 931 \approx 2,920.54 \text{ square centimeters} \]

Rounding the result gives us:

\[ \text{Surface Area} \approx 2,923.34 \text{ square centimeters} \]

Thus, the correct answer is:

2,923.34 square centimeters.