Question
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
1,884 square centimeters
1,884 square centimeters
1,648.5 square centimeters
1,648.5 square centimeters
942 square centimeters
942 square centimeters
109.9 square centimeters
To find the lateral surface area of the cone-shaped megaphone, we need to find the slant height of the cone first using the Pythagorean theorem. The slant height can be found using the radius and height of the cone.
Using the Pythagorean theorem: slant height^2 = radius^2 + height^2
In this case, the radius is 15 centimeters and the slant height is 20 centimeters.
20^2 = 15^2 + height^2
400 = 225 + height^2
height^2 = 400 - 225
height^2 = 175
height ≈ √175 ≈ 13.23
Now that we have the height of the cone (13.23 centimeters), we can calculate the lateral surface area of the cone.
Lateral surface area = π * radius * slant height
Lateral surface area = 3.14 * 15 * 20
Lateral surface area ≈ 942 square centimeters
Therefore, the correct answer is 942 square centimeters.