VJC P1 Q9

(i) Sketch the graph with equation $x^2 +(y-r)^2 = r^2$, where $r >0$ and $y \le r$

A hemispherical bowl of fixed radius $r$ cm is filled with water. Water drains out from a hole at the bottom of the bowl at a constant rate. When the depth of water if $h$cm (where $h \le r$).

(ii) Use your graph in (i) to show that the volume of water in the bowl is given by $V = \frac{\pi h^2}{3} (3r-h)$.

(iii) Find the rate of decrease of the depth of water in the bowl, given that a full bowl of water would become empty in 24 s,

(iv) without any differentiation, determine the slowest rate at which the depth of water is decreasing.