The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. If the width is changed by a scale factor of 1/3, then the new width is (1/3)w. The length and height remain the same. Therefore, the new volume of the rectangular prism is:
V' = l(1/3w)h
Multiplying both sides by 3 to simplify the expression, we get:
3V' = lw(3h)
Since the original volume of the rectangular prism is 768 ft3, we have:
V = lwh = 768
Multiplying both sides by 3 to simplify the expression, we get:
3V = lw(3h)
Substituting 3V for lw(3h), we get:
3V' = 3V(1/3w) = Vw
Therefore, the new volume of the rectangular prism is:
V' = Vw = (768 ft3)(1/3) = 256 ft3
So, the volume of the same shape if the width is changed by a scale factor of 1/3 is 256 ft3.