Question

1
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a cylinder is sliced by a plane that is not parallel to the base and intersects only the lateral surface. the resulting cross section is
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Explanation:

Step1: Analyze the properties of a cylinder

A cylinder has two circular bases and a lateral surface. When a plane slices a cylinder, different orientations of the plane give different cross - sections.

Step2: Consider the given slicing condition

If the plane is not parallel to the base and intersects only the lateral surface, we can use the concept of conic sections. For a right - circular cylinder (a common type), when a plane cuts the lateral surface at an angle (not parallel to the base), the cross - section satisfies the equation of an ellipse. Mathematically, if we consider the parametric equations of a cylinder \(x = r\cos\theta\), \(y = r\sin\theta\), \(z = z\) (in cylindrical coordinates) and a non - parallel plane \(z=ax + by + c\), substituting \(x\) and \(y\) gives a second - degree equation in \(x\) and \(y\) of the form \(Ax^{2}+Bxy + Cy^{2}+Dx + Ey+F = 0\) which represents an ellipse (since for a non - degenerate case and for a cylinder, \(B^{2}-4AC<0\)).

Answer:

An ellipse.