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Answer:
∛(2500π)√37 m² ≈ 120.911 m²
Step-by-step explanation:
If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...
V = 1/3πr²h
V = 1/3πr²(6r) = 2πr³
For a volume of 100 m³, the radius is ...
100 m³ = 2πr³
r = ∛(50/π) m
The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:
s² = r² +(6r)² = 37r²
s = r√37
Then the lateral area is ...
LA = πrs
LA = π(∛(50/π) m)(∛(50/π) m)√37
LA = ∛(2500π)√37 m² ≈ 120.911 m²
