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If you double the cross-sectional area and halve the length, you will still have the same volume but the dimensions will be different.

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Q: How can 2 prisms have the same volume but different dimensions?
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Is it possible for two rectangular prisms to have the same volume but not the same measurements?

Two different rectangular prisms can both have the same volume of 72 cm3


Two rectangular prisms that have the same volume and the same height would their base be different or the same?

They would have to have the same base area, if that's what you mean.


What are the dimensions of two rectangular prisms with the same surface area?

Given the surface area of a rectangular prism, there are infinitely many rectangular prisms possible.


Would the surface area of a triangular prism stay the same even if the dimensions were different?

No. There is no reason for the surface area of all triangular prisms to be the same always. For example, increasing the length of the prism only adds area; there is nothing to counteract this increase, so the area must be different.The same applies to all prisms and 3-dimensional objects: changing the dimensions can alter the area.


How are volume and surface area the same?

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.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.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.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.