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G-GMD.1 Core M2-037-R07-V03

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

Recover pyramid volume from a matched prism

Problem

A square pyramid has base area \(48~\text{in}^{2}\) and perpendicular height \(10~\text{in}\). Calculate the volume of a matched prism, apply the pyramid-to-prism factor of \(\text{one}~\text{third}\), and report the pyramid's volume.

Square pyramid with base area 48 in² and perpendicular height 10 in. 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