Problem

A right circular cylinder has base radius \(R\). An interior plane parallel to \(\text{both}~\text{bases}\) cuts the cylinder. Use the diagram to state the plane orientation, surfaces met, cross-section shape, and dimensions.

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What this problem is really about

Classify a cylinder section from both the plane's orientation and the surfaces it meets. An interior plane parallel to the bases lies at one height, and the cylinder wall stays a constant radius from the axis at every height. Judge the true shape in the slicing plane itself, since perspective can make a constant-radius boundary look oval on the page.

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The plane is parallel to the bases, meets only the curved lateral surface, and forms a circle of radius R.

The plane is parallel to the bases, meets both bases and the curved lateral surface, and forms a rectangle of width 2R.

The plane is parallel to the bases, meets only the curved lateral surface, and forms a noncircular ellipse whose dimensions depend on the plane's height.

The plane is parallel to the bases, meets only the curved lateral surface, and forms a circle of radius R/2.

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A right circular cylinder has base radius \(R\). An interior plane parallel to \(\text{both}~\text{bases}\) cuts the cylinder. Use the diagram to state the plane orientation, surfaces met, cross-section shape, and dimensions.

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