Back to Apply geometry to design problems — Problem 2 · Task Set 43

Exercises: Apply Geometric Methods to Solve Design Problems

Show your work for each problem. When a problem asks you to round, round to the place the
problem names. Several problems ask you to explain a design decision rather than compute a
number — for those, write in complete sentences.

Grade 10·23 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-mg-a-3

Work through problems with immediate feedback

Fluency Practice

A designer wants a cylindrical can to hold $900$ cm $^3$ using as little metal as possible. Which quantity should the designer minimize?

The volume $\pi r^2 h$ , because a can that encloses less space is a smaller object overall, and smaller objects are built from less material.

The surface area $2\pi r^2 + 2\pi r h$ , because the metal forms the skin of the can and its area is what gets cut from the sheet.

The radius $r$ , because the circular top and bottom are the costly parts, and shrinking the radius shrinks both of them at once.

The height $h$ , because the curved side is a rectangle whose length is the height, so a shorter can needs a shorter strip of metal wrapped around it.