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G-GMD.4 Warmup M3-037-A06-V04

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

A rectangle is revolved around a line in the same plane that is parallel to \(\text{one}~\text{of}~\text{its}~\text{sides}\) and lies \(2~\text{units}\) away from the rectangle, without touching it. What solid is formed?

Prompt diagram for M3-037-A06-V04: the generating region, rotation axis, dimensions, and 360-degree sweep with the resulting solid withheld. Open full size
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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