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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