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IAL 2021 June Q3

A Level / Edexcel / P4

IAL 2021 June Paper · Question 3

题目

Problem

A bowl with circular cross section and height 20 cm is shown in Figure 2.

The bowl is initially empty and water starts flowing into the bowl.

When the depth of water is hh cm, the volume of water in the bowl, VV cm3^3, is modelled by the equation

V=13h2(h+4)0≤h≤20V=\frac{1}{3}h^2(h+4)\qquad 0\leq h\leq 20

Given that the water flows into the bowl at a constant rate of 160 cm3^3 s−1^{-1}, find, according to the model,

(a) the time taken to fill the bowl,

(2)

(b) the rate of change of the depth of the water, in cm s−1^{-1}, when h=5h=5

(5)
题目中文翻译

图 2 显示了一个圆形横截面、高度为 20 cm 的碗。

该碗最初是空的，水开始流入碗中。

当水深为 hh cm 时，碗中水的体积 VV cm3^3 可由下式建模：

V=13h2(h+4)0≤h≤20V=\frac{1}{3}h^2(h+4)\qquad 0\leq h\leq 20

已知水以恒定速率 160 cm3^3 s−1^{-1} 流入碗中，求根据该模型：

(a) 装满碗所需的时间；

(b) 当 h=5h=5 时，水深的变化率，单位 cm s−1^{-1}。

解答