What is the lateral area of the cone to the nearest whole number? The figure is not drawn to scale.
A cone is shown with the diameter of the circular base labeled 160 meters and the height of the cone labeled 60 meters.
(1 point)
Responses
15,080 m2
15,080 m 2
25,133 m2
25,133 m 2
45,239 m2
The lateral area of a cone can be calculated using the formula L = πrs, where r is the radius of the base and s is the slant height of the cone.
Given that the diameter of the base is 160 meters, the radius would be half of that, which is 80 meters.
To calculate the slant height (s), we can use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = 80^2 + 60^2
s^2 = 6400 + 3600
s^2 = 10000
s = √10000
s ≈ 100 meters
Now, we can calculate the lateral area using L = πrs:
L = π * 80 * 100
L ≈ 25133 m^2
Therefore, the lateral area of the cone is approximately 25,133 m^2, which is the second answer choice.