By Pappus's second theorem, the volume of a solid formed by rotating plane area A through angle 2pi about an external axis at centroidal distance bar d is:

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Mechanical Engineering QUESTION #2541

Question 1

By Pappus's second theorem, the volume of a solid formed by rotating plane area \(A\) through angle \(2\pi\) about an external axis at centroidal distance \(\bar{d}\) is:

\(V=\pi\bar{d}^2 A\)
\(V=2\pi\bar{d}A\)✔️
\(V=4\pi\bar{d}A\)
\(V=\frac{A}{2\pi\bar{d}}\)

Correct Answer Explanation

Pappus's second theorem: \(V=\theta\cdot\bar{d}\cdot A\). For a full revolution (\(\theta=2\pi\)): \(V=2\pi\bar{d}A\), where \(\bar{d}\) is the distance from the area's centroid to the axis of revolution.

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