hemispherical bowl question?

Question

a hemispherical bowl has a radius of 30cm. Water is poured into the bowl to a depth of 12cm. Calculate the radius of the surface of the water.

thank you

Answer 1

if we call x the radius to calculate we can express the volume of water as
1/6pi*h*(3x^2+h^2)= 1/3pih^2(3r-h) so

1/2 (3x^2+144)= 12*(90-12)

3/2x^2 +72=936 so x^2 = 576 and x=24cm