Doubling the diameter of a round duct increases its cross-sectional area by how many times?

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Multiple Choice

Doubling the diameter of a round duct increases its cross-sectional area by how many times?

Explanation:
Doubling the diameter makes the cross-sectional area grow by a factor of four. The area of a circle depends on the square of its diameter: A = (π/4) d^2. When the diameter becomes 2d, the new area is A' = (π/4) (2d)^2 = 4 (π/4) d^2 = 4A. Since doubling the diameter also doubles the radius, and area scales with the square of the radius, the increase is 2^2 = 4.

Doubling the diameter makes the cross-sectional area grow by a factor of four. The area of a circle depends on the square of its diameter: A = (π/4) d^2. When the diameter becomes 2d, the new area is A' = (π/4) (2d)^2 = 4 (π/4) d^2 = 4A. Since doubling the diameter also doubles the radius, and area scales with the square of the radius, the increase is 2^2 = 4.

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