Question

Find the surface area of each shipping package. Which package has the greater surface area? Does the same package have a greater volume?

package A: 14 x 12 x 3
package B: 11 x 6 x 8

Answer 1

• greater area: A
• no, B has the greater volume

Explanation:

The relevant area and volume formulas are ...

A = 2(LW +H(L +W))

V = LWH

When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.

Figure A has the larger area.

Figure B has the larger volume.

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Additional comment

The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)