There is a hemispherical bowl of diameter 30 cm and it is filled with water such that the radius the top surface of water is 9 cm. Find the height of the water and and the volume of water in the bowl. I could find the height using Pythagoras Theorem . However I cant find the volume .

  • $\begingroup$ I think you need some calculus to solve the problem for the volume $\endgroup$ – user Nov 27 '17 at 14:34
  • $\begingroup$ @gimusi so how do you do it $\endgroup$ – Ishaan Parikh Nov 27 '17 at 15:17
  • 1
    $\begingroup$ by integration, you can find some inspiration here youtube.com/watch?v=Rib7yyn81BY $\endgroup$ – user Nov 27 '17 at 15:23

Wikipedia on spherical cap has the volume formula $$V=\frac 16\pi h(3a^2+h^2)$$ with a derivation. $h$ is the height you calculated and $a$ is the radius of the base.

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