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
45,239 m 2
50,265 m2
50,265 m 2
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To find the lateral area of a cone, we need to find the circumference of the base and multiply it by the slant height of the cone.
The circumference of the base is equal to the diameter multiplied by π. In this case, the diameter is 160 meters, so the circumference is 160π meters.
The slant height is the hypotenuse of a right triangle formed by the height of the cone and the radius of the base. We can use the Pythagorean theorem to find the slant height. The radius is half the diameter, so it is 80 meters.
Using the Pythagorean theorem, we have:
(80^2) + (60^2) = (slant height^2)
6400 + 3600 = (slant height^2)
10000 = (slant height^2)
√10000 = slant height
slant height ≈ 100 meters
Now we can find the lateral area by multiplying the circumference of the base by the slant height:
lateral area = 160π meters * 100 meters
lateral area ≈ 16000π meters^2
To the nearest whole number, the lateral area is approximately 50,265 m^2.