Question

两道AP微积分题..

1 the volume of a cone of radius r and height h is given by V=1/3πr^2 if the radius increase at a constant rate of 1/2 centimeter per second, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
2 the volume of a cylindrical tin can with a top and a bottom is to be 16π cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?
麻烦用微积分方法解啦...我是帮别人问所以麻烦详细一点 感激不尽！

Answer 1

1) V = (1/3)πr^2 h
如果高度不变，只是半径增加，那么方程两边对时间求导得，
V' = (2/3)πrr' h = (2/3)π(6)(1/2)*9 = 18π cm^3/sec

2) A = 2π r^2 + 2π r h
限制条件：V = π r^2 h = 16π
=> h = 16/r^2 代入面积表达式，

A = 2π r^2 + 2π 16/r
对r求导，并令A' = 0,
2r - 16/r^2 = 0
r = 2 inches
h = 16/r^2 = 4 inches

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Answer 2

这是火星语吗，不懂啊