Question

An ice cube with a 10 cm side is melting so that its volume decreases by 12 cm/m. How fast is its surface area changing? ​

Answer 1

Answer:

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