Let the initial width, depth and height of the prism be w, d, and h respectively.
surface area of a rectangular prism is 2(w d + w h + d h).
After quadrupling the dimentions, new dimentions is 4w, 4d and 4h.
New surface area is 2(4w 4d + 4w 4h + 4d 4h) = 2(16 w d + 16 w h + 16 d h) = 16 2(w d + w h + d h)
Ratio of old surface area to new surface area is 2(w d + w h + d h) : 16 2(w d + w h + d * h) = 1 : 16
