Question

a box of crackers has a volume of 48 cubic inches. what is the volume of a similar box that is smaller by a scale factor of 2/3

Answer 1

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