Consider a cube of side cm whose volume is cm

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Consider a cube of side

a

cm whose volume is

V=a^{3}

^{3}

. (i) Differentiate

V

with respect to time

t

and write the relation between

\dfrac{dV}{dt}

and

\dfrac{da}{dt}

. (ii) If

\dfrac{dV}{dt}

is negative, explain what this implies about the sign of

\dfrac{da}{dt}

and hence about the physical behaviour of the cube. (iii) A student asserts, “Whenever

\dfrac{dV}{dt}

is decreasing,

\dfrac{da}{dt}

must remain constant.” Examine this statement and give a reasoned comment on its correctness.