Calculus - Related Rate 1
2013-12-01 10:00 pm
A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is a constant.
回答 (1)
2013-12-01 10:06 pm
✔ 最佳答案
V = (4/3)πr^3A = 4πr^2
We know that dV/dt = K(4πr^2) where K is a constant
On the other hand, dV/dt is also equals to dV/dr * dr/dt
= 4πr^2 * dr/dt
So, 4πr^2 * dr/dt = K(4πr^2)
or dr/dt = K
That is, the rate of change of the radius is a constant
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