A cone-shaped megaphone has a radius of 15 centimeters and a slant height of 20 centimeters. A megaphone has an open bottom. What is the lateral surface area of the megaphone, in square centimeters? Use 3.14 for pi.(1 point)
Responses
109.9 square centimeters
109.9 square centimeters
942 square centimeters
942 square centimeters
1,884 square centimeters
1,884 square centimeters
1,648.5 square centimeters
To find the lateral surface area of the megaphone, we need to find the slant height of the cone's lateral surface and then use it to calculate the lateral surface area.
The slant height of a cone can be found using the Pythagorean theorem:
h = sqrt(r^2 + l^2), where r is the radius and l is the slant height.
Plugging in the values r = 15 cm and l = 20 cm, we can calculate the slant height:
h = sqrt(15^2 + 20^2) = sqrt(225 + 400) = sqrt(625) = 25 cm
Now that we have the slant height, we can calculate the lateral surface area using the formula:
Lateral surface area = π * r * l = 3.14 * 15 cm * 25 cm = 1177.5 square centimeters
Therefore, the correct answer is 1,177.5 square centimeters.