Problem

An object's mass is \(m(V)=8V~\text{grams}\) when its volume is \(V~\text{cubic}~\text{centimeters}\). Form \(D(V)=m(V)/V\) and simplify it. State the density units, retain the restriction inherited from the original quotient, give the physical volume domain, and interpret the constant result.

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quotient expression=D(V)=8V; simplified=8V; output units=grams/cm³; algebraic restriction=none; contextual domain=V>0; interpretation=fails to divide mass by volume

quotient expression=D(V)=m(V)/V=8V/V; simplified=D(V)=8; output units=grams/cm³; algebraic restriction=V≠0; contextual domain=V>0; interpretation=constant density8g/cm³ for positive volume

quotient expression=D(V)=8V/V; simplified=8; output units=grams total; algebraic restriction=V≠0; contextual domain=V>0; interpretation=incorrectly retains mass units

quotient expression=D(V)=8V/V; simplified=8; output units=grams/cm³; algebraic restriction=V≠0; contextual domain=V∈(-∞,0)∪(0,∞); interpretation=allows negative volume

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An object's mass is \(m(V)=8V~\text{grams}\) when its volume is \(V~\text{cubic}~\text{centimeters}\). Form \(D(V)=m(V)/V\) and simplify it. State the density units, retain the restriction inherited from the original quotient, give the physical volume domain, and interpret the constant result.

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