In my truck, I'm moving a rectangular solid whose volume is 105.?

Question

In my truck, I'm moving a rectangular solid whose volume is 105. If the length of each edge is a prime, what is the total surface area (the sum of the areas of all 6 faces) of the rectangular solid?

Answer 1

The solid has dimensions of 3,5 and 7.

The total surface area is:

A = 2(7x5 + 7x3 + 3x5) = 142 square units

Answer 2

The sides are 7, 5 and 3 (the three prime factors in 105).

So area is (3*5 + 3*7 + 5*7) * 2 = 142