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: _____________________________ 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: _____________________________________________________ " V = (5 cm)³ = 5 * 5 * 5 * cm³ = 125 cm³ " ; _____________________________________________________ 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"). _____________________________________________________ So, V = (10 cm)³ = 10 * 10 * 10 * cm³ = 1000 cm³ . ______________________________________________________ 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. ________________________________________________ So; (10 cm)³ ≠ 2* (5 cm)³. _________________________________________________
