Problem preview
G-GMD.4 Warmup M3-037-A09-V01

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

Match a rotated 2D figure to the 3D solid it forms

Problem

What \(3D\) solid is formed by rotating a rectangle about \(\text{one}~\text{side}\)?

Big Picture

What this problem is really about

Fix the stated side as the axis and examine crosswise segments of the filled rectangle. Each has the same length, so every one sweeps a filled disk of the same radius, and those disks extend along the full axis-side length. Classify the disk stack from its constant radius, noting that no taper develops anywhere along the axis.

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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
Match a rotated 2D figure to the 3D solid it forms