What's the lateral area of a right circular cone if the diameter of the base is 4 m and the slant height of the cone is 15m? Round your answer to the nearest whole number.
Mathematics · High School · Tue Nov 03 2020
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Given:
Diameter = 4m
Slant height of the cone = 15 m
Determine the lateral area:
Formula for the lateral area of right circular cone:
AL=πr √(h^2+r^2)
Solution:
Since we are given the diameter of the cone we must first determine the radius of the cone. Diameter is equal to 2 times the radius.
D = 2r
Therefore, radius is half the diameter
r = d/2
r = 4m / 2
r = 2m
Now that we have the value of the radius we can solve the lateral area of the cone, by substituting the values of the radius and the height.
AL=πr √(h^2+r^2)
AL=π(4) √(15^2+4^2)
AL=4π √(225+16)
AL=4π √(241)
AL = 62.1π
AL = 195.1 m^2
Final answer: The lateral area of the cone is 195.1 m^2