If the diameter of a pipe increases while keeping the length constant, how does the volume of the pipe change?

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Prepare for the New York City Refrigeration License Exam I. Utilize flashcards, multiple-choice questions, and detailed explanations to boost your readiness. Ace your licensing exam!

Multiple Choice

If the diameter of a pipe increases while keeping the length constant, how does the volume of the pipe change?

Explanation:
Think of the pipe as a cylinder. With the length fixed, the volume is the cross-sectional area times the length. The cross-sectional area of a circle is πr^2, and with diameter d, r = d/2, so area = π(d/2)^2 = (π/4) d^2. Multiplying by the fixed length L gives V = (π/4) d^2 L. That means the volume grows with the square of the diameter—twice the diameter makes four times the volume, all else equal. So the correct idea is that the volume increases proportional to the square of the diameter.

Think of the pipe as a cylinder. With the length fixed, the volume is the cross-sectional area times the length. The cross-sectional area of a circle is πr^2, and with diameter d, r = d/2, so area = π(d/2)^2 = (π/4) d^2. Multiplying by the fixed length L gives V = (π/4) d^2 L. That means the volume grows with the square of the diameter—twice the diameter makes four times the volume, all else equal. So the correct idea is that the volume increases proportional to the square of the diameter.

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