The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. What is the total number of white cubes that were used to build the prism?

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We can count the number of cubes on each edge of the prism. This is a $5\times6\times7$ cube.

$$V = lwh$$ $$V = 5(6)(7) = 210$$

Since the black and white cubes alternate, half of the cubes will be white.