Problem preview

G-GMD.1 Core M2-037-R05-V04

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

Build prism and cylinder volume from congruent layers

Problem

An oblique cylinder and a right cylinder \(\text{both}~\text{have}~\text{radius}~2~\text{ft},~\text{perpendicular}~\text{height}~9~\text{ft}\), and matching horizontal cross-sections at every level. Use the layer or Cavalieri argument to compare their volumes and calculate each exact volume.

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Each volume is (1/3)Bh = 12π ft³.

The oblique cylinder has a different volume despite equal bases and perpendicular heights.

They have equal volumes: each is Bh = (4π)(9) = 36π ft³.

Their volumes cannot be determined without their slanted edges.

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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: Build prism and cylinder volume from congruent layers