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G-GMD.1 Core M2-037-R09-V04

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

Build volume by accumulating cross-sections

Problem

A solid on \(0~\le~x~\le~3\) has square cross-sections of side \(x\), so each slice area is \(x^{2}\). Interpret the supplied limit of the area-times-thickness sum, equal to \(9\), and state the volume with correct units.

Solid extending from x=0 to x=3 with square cross-sections perpendicular to the x-axis, each square having side length x, and a supplied limit of Σxᵢ²Δx equal to 9. 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
Build volume by accumulating cross-sections