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M3-037-A03-V03
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G-GMD.4
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M3-037-A03-V03
Identify cross-sections of 3D objects and solids generated by rotating 2D objects.
Classify a fully specified cylinder cross-section
Problem
A finite right circular cylinder is tall enough that an oblique plane makes a closed intersection through the curved lateral surface and meets neither base. Use the diagram to classify the section and state what determines its dimensions.
Answer choices
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A
The plane is oblique to the bases, meets only the curved lateral surface, and forms a circle of radius R whose dimensions do not depend on the plane tilt.
B
The plane is oblique to the bases, meets both bases and the curved lateral surface, and forms a rectangle of width 2R and the cylinder's full height.
C
The plane is oblique to the bases, meets only the curved lateral surface, and forms a noncircular ellipse whose dimensions depend only on cylinder height, not on R or plane tilt.
D
The plane is oblique to the bases, meets only the curved lateral surface, and forms a noncircular ellipse with dimensions determined by R and the plane tilt.
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Curriculum context
Standard G-GMD.4
Category Geometry
Domain Geometric Measurement and Dimension
Objective Identify cross-sections of 3D objects and solids generated by rotating 2D objects.
Problem type Classify a fully specified cylinder cross-section
