To find the mass of a shoe, you would need a scale, in order to measure the weight of the shoe first. Its mass will then be m = weight / g where g is the gravitational acceleration 9.8 m/s2.
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A shoe is only slightly larger than the foot that uses the shoe.
That depends on the dimensions of the shoe box, now doesn't it? It's the product of the three dimensions.
I guess it depends on the kind of shoe box. Let's take a regular shoe box with six rectangular sides. Let the dimensions be a x b x c The surface area is 2(ab + ac + bc) Intuitively, you have three different dimensions, a, b, and c. So each panel has area of ab, ac, or bc. Then if you look at opposite sides of the box, you see two opposite sides are the same, so you multiply the sum by two.
That is a rectangular solid.
Rectangular prism.