Random Questions from 2016 Prelims #7

Random Questions from 2016 Prelims #7

JC Mathematics

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.