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What is the shape of the cross section formed when a cylinder is cut by a plane parallel to its base?

A. Rectangle
B. Circle
C. Ellipse
D. Triangle

1 Answer

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Final answer:

The cross section formed when a cylinder is cut by a plane parallel to its base is a circle, as the points on the cut are equidistant from the axis, making the cross section circular.

Step-by-step explanation:

When a cylinder is cut by a plane parallel to its base, the shape of the cross section formed is a circle. This occurs because the cutting plane is parallel to the base, which means every point on the cut surface is equidistant from the cylinder's central axis, forming a perfect circle.

Cylinders, being three-dimensional objects with parallel sides, have a simple relationship between their volume and cross-sectional area, where the volume (V) is the cross-sectional area times the height (V = Ah). In context to conic sections, if a cylinder is seen as a cone with a top of the same size as its base, cutting it with a plane parallel to the base will always result in circular cross-sections, as opposed to other conic sections like ellipses, parabolas, and hyperbolas that result from different angles of cutting planes on cones.

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