The volume of a melting cube is decreasing at a rate of 10cm^3/min. How fast is the surface area of the ice cube decreasing when the length of an edge is 30 cm?

Answer 1

V = x^3
dV/dt = 3x^2 dx/dt
10 = 3x^2 dx/dt
dx/dt = 10/(3x^2)

SA = 6x^2
d(SA)/dt = 12x dx/dt
dx/dt = d(SA)/dt / (12x)

d(SA)d/t / (12x) = 10/(3x^2)
d(SA)/dt = 120x/(3x^2)
which when x = 30
= 120(30)/2700 = 4/3 cm/min

Answer 2

Thank you so much that was so helpful.