MathDB
The Amazing Prime

Source: UMD 2023 I #9

October 26, 2023
UMDgeometry

Problem Statement

The Amazing Prime company ships its products in boxes whose length, width, and height (in inches) are prime numbers. If the volume of one of their boxes is 105105 cubic inches, what is its surface area (that is, the sum of the areas of the 6 sides of the box) in square inches? a. 21b. 71c. 77d. 05e. 142 \mathrm a. ~ 21\qquad \mathrm b.~71\qquad \mathrm c. ~77 \qquad \mathrm d. ~05 \qquad \mathrm e. ~142