Quandaries and Queries


Can you please tell me if the volume and surface area of a prism can ever be the same? Could you please explain why or why not.
Thanks so much!


Hi Melissa,

This is strange question - with some interesting possibilities:

- if we are in 'science' and 'measurement' then we watch the 'units':
area is square units, and volume is units cubed (e.g. cm2 vs cm3). With that perspective, the measurements cannot have the same units.

- if we just look at the numbers (not the units) then the answer is certainly.

Consider the impact of scaling.

If I have an initial object, with volume V and surface area S, then scaling everything up by 2, I have volume 8 V and surface area 4 S. They do not change at the same rate!

If I scale by k, then we have k3 V and k2 S.
In order for k3 V to equal k2 S, or k V = S, all I need is for k = S/V! So there is a scaled version where they are the same number.

Of course, if you switch your unit of measurement (e.g. from cm to m) this 'equality' will vanish and you will need to scale the object up to match the new units!

Walter Whiteley


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