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Answer:
∛(2500π)√37 m² ≈ 120.911 m²
Step-by-step explanation:
If the height of the cone is three times the diameter, that means it is six times the radius. Hence, the volume is computed as...
V = 1/3πr²h
V = 1/3πr²(6r) = 2πr³
To find the radius for a volume of 100 m³, solve...
100 m³ = 2πr³
r = ∛(50/π) m
To calculate the lateral area, the slant height must be found using the Pythagorean theorem:
s² = r² +(6r)² = 37r²
s = r√37
Thus, the lateral area is calculated as...
LA = πrs
LA = π(∛(50/π) m)(∛(50/π) m)√37
LA = ∛(2500π)√37 m² ≈ 120.911 m²
