Problem preview

MF.GM.7 Standard MF-054-A11-V04

Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.

Put both geometry situations into one modeling language

Problem

A cylinder has radius \(3~\text{cm}\) and height \(8~\text{cm}\). A rectangular block is \(9~\text{cm}~by~4~\text{cm}~by~2\pi~\text{cm}\). Which complete response correctly compares the volumes?

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Situation A: volume; V = πrh = π(3)(8) = 24π cm³. Situation B: volume; V = lwh = (9)(4)(2π) = 72π cm³. Final judgment: not equal.

Situation A: volume; V = πr²h = 72π cm³. Situation B: volume; V = lwh = 72π cm³. Final judgment: not equal, because the formulas are different.

Situation A: volume; V = πr²h = π(3²)(8) = 72π cm³. Situation B: volume; V = lwh = (9)(4)(2π) = 72π cm³. Final judgment: equal.

Situation A: volume; V = πr²h = π(3²)(8) = 72π cm³. Situation B: volume; V = lwh = (9)(4)(2) = 72 cm³. Final judgment: not equal.

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Curriculum context

Course: Math Foundations
Standard: MF.GM.7
Category: Geometry and Measurement
Domain: Modeling
Objective: Set up and solve contextual measurement problems that require choosing the correct geometric formula and units.
Problem type: Put both geometry situations into one modeling language