Question

All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is (a) 1 centimeter? (b) 10 centimeters?

Answer 1

\[V=e^3\]
\[\frac{ dV }{ dt }=(3e^2)\left( \frac{ de }{ dt } \right)\]
So When e =cm
\[\frac{ dV }{ dt }=3(1cm)^2*(3cm/s)=9cm^3/s\]

And when e = 10cm
\[\frac{ dV }{ dt }=3(10cm)^2*(3cm/s)=900cm^3/s\]

Answer 2

Ah! Alright! Thanks!