Problem preview
G-GMD.4 Warmup M3-037-A06-V01

Identify cross-sections of 3D objects and solids generated by rotating 2D objects.

Identify the solid formed by revolving a rectangle around a parallel line

Problem

What solid is formed by revolving a rectangle around \(\text{one}~\text{of}~\text{its}~\text{sides}\)?

Big Picture

What this problem is really about

Track the entire filled rectangle, not just its boundary, as one side remains fixed. At each position along that axis, the perpendicular segment sweeps a filled disk whose radius is the rectangle's width; those congruent disks extend along the axis-side length. Classify the resulting solid from this constant-radius stack and map the original dimensions to radius and height.

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Four variants of this problem type
Curriculum context
Course
Math III
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
Identify the solid formed by revolving a rectangle around a parallel line