The most economical proportion for a right circular cone is to have its height three times long as its base diameter. What later

Question

2 years ago

8

al area of the cone would produce a volume of 100m^3.

1 answer:

defon · Answer 1 · 2023-10-12T20:42:30+03:00

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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