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Back to Apply geometry to design problems — Problem 3 · 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
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Fluency Practice

A U-shaped curve of surface area against radius for a fixed-volume cylinder, with four marked points
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A cylindrical can must hold 500500 cm3^3. For each radius below, the height is found from h=500πr2h = \dfrac{500}{\pi r^2} and the surface area from SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi r h. Complete the table by giving each surface area in square centimeters, rounded to the nearest tenth.

At r=3r = 3 cm the surface area is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cm2^2. At r=4r = 4 cm it is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cm2^2. At r=5r = 5 cm it is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cm2^2. At r=6r = 6 cm it is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   cm2^2.

surface area at r = 3:
surface area at r = 4:
surface area at r = 5:
surface area at r = 6: