If a snowball melts so that its surface area decreases at a rate of 1cm^2/min,
find the rate at which the diameter decreases when the diameter is 10cm.
同埋please give the explanation.
超難的數學Word Problem!!!!!!!! 請高手入
2012-02-10 12:51 pm
回答 (1)
2012-02-10 4:34 pm
✔ 最佳答案
Assume the snowball is a perfect sphere, so surface area of a sphere, S = 4pr^2, where r = radius of sphere. Since diameter, x = 2r, so r = x/2.
That is S = 4p(x/2)^2 = px^2
dS/dt = 2px (dx/dt)
dS/dt = - 1, x = 10
so rate of change of diameter, dx/dt = -1/2p(10) = - 1/20p cm/min.
收錄日期: 2021-05-01 14:03:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120210000051KK00078