Question

The volume of a cone is said to be 36pi. All that is told is the water level goes up to H/2.
What is the volume of the water?

Answer 1

V = (1/3)π r^2 h = 36π
r^2 h = 108

Now if we cut the height in half, then the radius is also cut in half

new volume = (1/3)π(r/2)^2 (h/2)
= (1/24)π r^2 h
= (1/24)π(108) = 9π/2

or

the volume of similar solids is proportional to the cube of their sides
so (1/2)^3 = 1/8

so the new volume is (1/8)(36π) = 9π/2