Explanation:
I assume the changes to the dimensions were made by using the same factor for each dimension, right ?
so, what do we need to do or calculate ? what is the desired result ?
the surface areas ? the new dimensions ? the volume ?
or only the factor of how much the dimensions changed, when the surface area was changed to 1/4 ?
????
I assume the last one, because there is so little information about what to do.
the surface area is calculated based on the areas of the various rectangles in the surface of the object.
each rectangle area is the result of multiplying 2 dimensions.
as the whole surface area shrinks by the factor 1/4, it means that every rectangle on the surface also shrinks by the factor 1/4.
and this factor 1/4 is the result of multiplying 2 dimensions. each dimension was changed by multiplying it with the same factor as every other dimension.
so, factor×factor = 1/4
factor² = 1/4
factor = sqrt(1/4) = 1/2
so, yes, in order to shrink the surface area to 1/4 of the original size, all the dimensions need to be cut in half (multiplied by 1/2).