Question

Gerardo says that a cube with edges that neasure 10 centimeters has a volume that is twice as much as a cube with sides that measure 5 centimeters. Explain and correct gerardos error

Answer 1

Answer:
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       The problem is that the "volume" of cube is equal to the length of one of its sides, "cubed" ;  that is,  "V = s³ " .    

A cube with with sides that measure 5 cm has the following volume:
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         " V  =  (5 cm)³  =  5 * 5 * 5 * cm³  =  125 cm³ " ;
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The volume of cube with sides that measure "10 cm" 
      (which is, in fact, has "side lengths that are TWICE the value of  "5 cm" ; gets "cubed" — as opposed to getting multiplied by "2"). 
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    So, V = (10 cm)³ = 10 * 10 * 10 * cm³ = 1000 cm³ .
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When we deal with "volume increases";  we are dealing with "three-dimensional objects",  with values of "cubic units" .  And in a cube, with all side lengths being equal, an increase in side length will result in an "exponential" increase in volume.
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So;  (10 cm)³   ≠  2* (5 cm)³.
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