surface area of a cube, side 'x' increasing at rate 6cm^2/min. What rate of the sides increasing at v=27cm ^3

Question

Surface area of a ice cube with side 'x' is increasing at rate of 6 cm^2/min. At what rate are the sides increasing at when the volume is 27cm^3.

Answer 1

the volume of cube is V=x^3
when v=27 therefore 27=x^3
take cube root both side we have x=3
you should know the formula for surface of cube is
S=6x^2
take derivative both sides which is respect to t
dS/dt=12xdx/dt
but you want to solve for dx/dt
dx/dt= dS/dt/(12x)
you know x=3, dS/dt= 6
therefore
dx/dt=6/(12*3)=1/6 cm/min
conclusion at v=27, rate of surface is 6cm^2/min therefore rates of side increasing 1/6 cm/min
good luck. bro