To find the surface area of a cone, we need to calculate the curved surface area (CSA) and the base area.
First, let's find the radius of the hat. The given diameter is 38 cm, so the radius is half of that, which is 38 cm / 2 = 19 cm.
Next, let's calculate the CSA. The slant height is 30 cm, and the radius is 19 cm. We can use the formula CSA = π * radius * slant height.
CSA = 3.14 * 19 cm * 30 cm
= 1794.6 cm² (rounded to one decimal place)
Now, let's find the base area. The base of a cone is a circle, so we can use the formula for the area of a circle, which is A = π * radius^2.
Base area = 3.14 * (19 cm)^2
= 3.14 * 361 cm²
= 1135.54 cm² (rounded to two decimal places)
Finally, let's add the CSA and base area together to get the surface area of the hat.
Surface area = CSA + base area
= 1794.6 cm² + 1135.54 cm²
= 2930.14 cm²
≈ 2930.1 cm²
Therefore, the correct answer is 2,930.1 square centimeters, which is closest to 2,923.34 square centimeters.
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.
Responses
2,923.34 square centimeters
8,113.76 square centimeters
3,579.6 square centimeters
1,789.8 square centimeters
1 answer