For this case what you need to know is that the original volume of the cookie box is: V = (w) * (l) * (h) Where, w: width l: long h: height. We have then: V = (w) * (l) * (h) = 48 in ^ 3 The volume of a similar box is: V = (w * (2/3)) * (l * (2/3)) * (h * (2/3)) We rewrite: V = ((w) * (l) * (h)) * ((2/3) * (2/3) * (2/3)) V = (w) * (l) * (h) * ((2/3) ^ 3) V = 48 * ((2/3) ^ 3) V = 14.22222222 in ^ 3 Answer: the volume of a similar box that is smaller by a scale factor of 2/3 is: V = 14.22222222 in ^ 3
