Related rates: The volume of a cube is increasing at the rate of 40 mm^3/s. How fast is the surface area of the cube increasing when each edge is 10 mm?

Answer 1

for a cube of side s,
v = s^3
dv/dt = 3s^2 ds/dt
Thus, ds/dt = 2/15 mm/s

a = 6s^2
so
da/dt = 12s ds/dt
da/dt = 16 mm^2/s