Random Questions from 2016 Prelims #7

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 hcm (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.

Showing 4 comments
  • Charles
    Reply

    Hi may I know the mark allocation for the sub-parts of this question? Is it possible to include the mark allocation for future questions too?

    • KS Teng
      Reply

      will try, cos i gave out 2016 prelims to my students and most of these solutions are meant for their independent checking.

  • Charles
    Reply

    Can I also confirm that “y le r” refers to “y is a real number”?

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