Calculus Question. Please Help!!!! BEST ANSWER!!!!
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Calculus Question. Please Help!!!! BEST ANSWER!!!!

[From: ] [author: ] [Date: 11-11-06] [Hit: ]
!!! Thanks.The diameter decreases at a rate of 1/(6π) cm/min ≈ 0.053 cm/min.......
If a snowball melts so that its surface area decreases at a rate of 4 cm^2/min, find the rate at which the diameter decreases when the diameter is 12 cm.

Please Help!!!! Thanks.

-
S = 4πr^2
dS/dt = 8πr dr/dt

d = 2r
dd/dt = 2 dr/dt

-4 cm^2/min = 8π(6 cm) dr/dt
-1/(12π) cm/min = dr/dt

The diameter decreases at a rate of 1/(6π) cm/min ≈ 0.053 cm/min.
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