What was the nature of the modification the student made? How do you know?

Question

A student has an object that has a volume of 64 cm cubed and its surface area is 128 cm squared. The student then modifies the object, without using any tools, so that its surface area is 88 cm squared,but the volume is still 64 cm cubed.

Answer 1

64 cm^3 for a cube = s^3 = 4^3. Each side is 4 cm. A cube has minimum surface area for a rectangular prisom

surface area = 6(4x4) = 96 cm^2.

for surface area of 128, the sides are slightly larger than 2x4x8. 2x4x8 has surface area 124

if surface area is reduced to 88 cm^2, that's less than 96 cm^2. That would require changing the shape from a rectangular prison to a different shape. Smallest surface area for 3 dimensions is a sphere, but it would have about 40 cm^2 for a volume of 64 cm^3.

To get 88 would mean making either a rounder object, maybe an ellipsoid or more than 6 sided object