题目
Problem
A tablet is dissolving in water.
The tablet is modelled as a cylinder, shown in Figure 1.
At seconds after the tablet is dropped into the water, the radius of the tablet is mm and the length of the tablet is mm.
The cross-sectional area of the tablet is decreasing at a constant rate of mm s
(a) Find
when
(4)
(b) Find, according to the model, the rate of decrease of the volume of the tablet when
(4)
题目中文翻译
一片药片正在水中溶解。
药片被建模为一个圆柱体，如图 1 所示。
药片投入水中 秒后，药片半径为 mm，长度为 mm。
药片横截面积正以恒定速率 mm s 减小。
(a) 当 时，求
。
(b) 当 时，根据该模型求药片体积的减小速率。