求高手解3道微积分题。。。谢谢

yolanda12

1. the radius of a cylinder is decreasing at a rate of 1 cm/min . the height remains the same as 20 cm . hoe fast is the volume changing when the radius is 12 cm?

2. a balloon is rising at a rate of 200 m/min . for every 500 m increase in height the air pressure causes the radius to increase 2 cm. find the rate of increase of the volume when the radius is 10 cm?

3. the dimension of a conical tank is of radius 3 m and height 6 m. what is added to is at a  rate of  (派) m^3/min . find the rate of change of wate level when the height is 3m?


需要过程。。。谢谢。

WTTO

1. volume=Pie x radius x radius x height.  v=pie x h x r^2
求导数 dv= pie x h x 2r x dr = 20 x 2 x 6 x 1 x pie = 240 pie

太久没用了，只记得一些概念。

WTTO

2. V=(4/3) x pie x r^3
dv=(4/3) x pie x 3 x r^2 x dr =4 pie x r^2 x dr = 4 pie x 10 x 10 x dr = 400 pie x dr
= 400 pie x (2/500 x 200) = 400 x 4/5 pie = 320 pie cm^3 / min

WTTO

3. As height = 2 * radius, volume = pie / 12 * height^3
dv=pie / 12 * 3 * h^2 * dh = pie / 4 * h^2 * dh
pie (ie dv) = pie / 4 * 3^2 * dh = pie / 4 *9 dh.
dh = 4/9 m/min