# Volume of Water in Hemisphere?

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 .

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