Yes many different shapes can have the same volume
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You need more information. There are many shapes which could hold the same volume, but have different (is it perimeter of the base, maybe?).
This will usually be the case for objects that have different shapes: even if they have the same volume, it is unlikely that they have the same surface area. As an example, calculate the volume and surface area of the following two rectangular block shapes: 1) A 2 x 2 x 2 rectangular block 2) A 1 x 1 x 8 rectangular block
No volume is for 3 dimensional shapes and area for two dimensions.
If they are the same shapes but differ only in size, then they are SIMILAR shapes. Otherwise, they are simply different shapes.
Yes - even shapes with different area.