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G-GMD.1 Core M2-037-R07-V04

Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.

Recover pyramid volume from a matched prism

Problem

\(\text{Two}~\text{pyramids}\) have equal base area \(30~\text{ft}^{2}\) and equal perpendicular height \(9~\text{ft}\) but different horizontal apex positions. Use matched cross-sections or the pyramid formula to compare their volumes and calculate each volume.

Two pyramids with different apex positions, equal base area 30 ft², and equal perpendicular height 9 ft. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GMD.1
Category
Geometry
Domain
Geometric Measurement and Dimension
Objective
Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.
Problem type
Recover pyramid volume from a matched prism