Question

If all three dimensions of a rectangular prism are quadrupled, then how will the new surface area compare to the old surface area? Write your answer as the ratio of two whole numbers separated by a colon; for example, "2:3".

Answer 1

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