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
109.9 square centimeters
109.9 square centimeters
942
To find the lateral surface area of a cone-shaped megaphone, you need to calculate the area of the curved surface that makes up the cone.
First, you'll need to calculate the slant height of the cone using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the radius and the height of the cone.
In this case, the radius is 15 centimeters and the slant height is 20 centimeters. Using the Pythagorean theorem (a^2 + b^2 = c^2), you can set up the equation as follows:
15^2 + h^2 = 20^2
225 + h^2 = 400
h^2 = 400 - 225
h^2 = 175
h = √175
h ≈ 13.23 centimeters (rounded to two decimal places)
Once you have the slant height, you can calculate the lateral surface area using the formula: lateral surface area = π × radius × slant height.
Plugging in the values:
lateral surface area = 3.14 × 15 × 13.23
lateral surface area ≈ 1,648.5 square centimeters
Therefore, the correct answer is 1,648.5 square centimeters.