Posted by **john** on Thursday, October 28, 2010 at 11:16pm.

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?

- calculus -
**Reiny**, Thursday, October 28, 2010 at 11:25pm
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

- calculus -
**Anonymous**, Sunday, March 6, 2016 at 3:49am
Thank you so much that was so helpful.

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