Problem preview
MF.GM.7 Challenge MF-054-A12-V03

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

Find every correct geometry model in a mixed set

Problem

A cylindrical can has radius \(4~\text{cm}\) and height \(11~\text{cm}\). Determine the metal needed for the entire closed can, including the top and bottom. Evaluate statements A–H, then report the complete set of statements that model the situation correctly.

A. This requires surface area because the material covers the can.
B. A valid formula is \(SA~=~2\pi~r^{2}~+~2\pi~\text{rh}\).
C. A valid setup is \(2\pi~(4)^{2}~+~2\pi~(4)(11)\).
D. Report the final result in \(\text{cubic}~\text{centimeters}\).
E. Use \(V~=~\pi~r^{2}h\) because the can holds soup.
F. The curved side alone, without the top and bottom, fully answers the question.
G. \(\text{Square}~\text{centimeters}\) are the appropriate units for the metal.
H. \(\pi~(4)^{2}(11)\) gives the metal needed for the closed can.

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Four variants of this problem type
Curriculum context
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
Find every correct geometry model in a mixed set