Can different shapes have the same volume and surface area?

The same principle is valid in 3D, with 5 cubes you can make a cross and rectangular cuboid with the same volume and area. The same is possible with 6 pyramids with equal sides, you can compose different shapes with the same surface area and volume, keeping the same number of border planes. So it is possible for some very special shapes. read more

Volume and surface area can never be the same because volume is a measure in 3-dimensional space whereas area is a measure in 2-dimensional space. The dimensions are different and so equality is not possible. read more