Question

A rectangular prism has a volume of 686 cubic units. How many unit cubes would fill the volume of the solid if they were packed without any gaps or overlaps?

Answer 1

2 unit cubes of 7 units side length can fill the volume of the solid without overlap

Explanation:

Volume of a cube is L^3

Let the number of cubes be n

Since the cubes are similar,

then;

nL^3 = 686

nL^3 = 343 * 2

By inspection

L^3 = 343 (since it is a perfect cube and the cube root is 7)

n = 2