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G-GMD.1 Core M2-037-R08-V03

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

Recover cone volume from a matched cylinder

Problem

A cone has base area \(81\pi~\text{in}^{2}\) and height \(7~\text{in}\). Calculate the matched cylinder's volume, apply the cone-to-cylinder factor of \(\text{one}~\text{third}\), and report the cone's exact volume.

Cone with base area 81π in² and perpendicular height 7 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 cone volume from a matched cylinder