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G-GMD.4 Warmup M3-037-A07-V04

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

Determine cone dimensions from a rotated right-triangle region

Problem

A filled right triangle with legs \(5~\text{cm}\) and \(12~\text{cm}\) rotates \(360°\) about the \(5~\text{cm}\) leg. Use the diagram to identify the solid and give its radius, height, slant height, and volume with units.

Prompt diagram for M3-037-A07-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
Determine cone dimensions from a rotated right-triangle region