The volume (in cm ) of a cube and its edge length (in cm) both change with time

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The volume

V

(in cm

^{3}

) of a cube and its edge length

a

(in cm) both change with time. At a particular instant, measurements give

\dfrac{dV}{dt}=60\,\mathrm{cm^{3}\,s^{-1}}

and

\dfrac{da}{dt}=0.5\,\mathrm{cm\,s^{-1}}

. (i) Calculate

\dfrac{dV}{da}

at that instant. (ii) Hence determine the length of an edge

a

of the cube at that moment.