what is the lateral area of the cone to the nearest whole number? the figure is not drawn to scale.
base=160 m
height=60 m
a) 15,080 m^2
b) 25,133 m^2
c) 45,239 m^2
d) 50,265 m^2
The lateral area of a cone is given by the formula: L = πrs, where r is the radius of the base and s is the slant height. To find the slant height, we use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = (80)^2 + (60)^2
s = √(6400 + 3600)
s ≈ 92.2 m (rounded to one decimal place)
Now we can calculate the lateral area:
L = πrs
L = π(80)(92.2)
L ≈ 23,023.7 m^2
Rounded to the nearest whole number, the lateral area is 23,024 m^2, which is closest to option b) 25,133 m^2. However, none of the given options is an exact match, so it's possible that there is an error in the question or answer choices.