GOZUNTA
Try it now
Problem preview
G-GMD.1 Core M2-037-R07-V02

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

Recover pyramid volume from a matched prism

Problem

A cube of side \(6~m\) is partitioned into \(\text{six}~\text{congruent}~\text{square}~\text{pyramids}\) whose common apex is the cube center. Calculate the cube volume and divide by \(\text{six}\); then verify the result using pyramid base area \(36~m^{2}\) and perpendicular height \(3~m\).

Cube with side length 6 m partitioned from its center into six congruent square pyramids, one based on each face. Open full size
Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now
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