A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is `tan^(-1)(0. 5)` . Water is poured into it at a constant rate of 5 cubic metre per hour. Find the rate at which

Explanation

Let `r, h` and `a` be the radius, height and the semi-vertical angle of the given conical water tank.



`Rightarrow tan a=frac{r}{h} `


`Rightarrow a=tan ^{-1}(frac{r}{h}) `


`text { As } a=tan ^{-1}(0.5) text { (given) }`


`text { Therefore, } frac{r}{h}=0.5 `


`Rightarrow r=frac{h}{2} quad cdots(1)`



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