find the depth of water in the tray.

Question

A cylindrical container of base diameter 8 cm placing in an empty cylindrical tray of base diameter 20 cm. The container is full of water. Then four identical metal cubes of sides 3 cm are sunk to the bottom of the container such that the water inside overflows into the tray. If all the water overflowed is collected in the tray, find the depth of water in the tray

Answer 1

Assuming the 8 cm cylinder is full of water, the volume of water that overflows will equal the amount of water displaced by the metal cubes (technically it would also depend on the type of metal but that's another problem).

 

The volume of one metal cube is V = s³ and since each side is 3 cm, V = 3³ or 27 cm³.  There are 4 cubes, so the total volume of displaced water is 4*27 = 108 cm³

 

Now since the 8 cm diameter cylinder is inside the 20 cm diameter cylinder, the amount of displaced water will have to fit inside the space between the two cylinders.

 

The volume of a cylinder is V = ∏r²h.  In this case the volume is 108 cm³ but the radius of the empty space is 10 cm - 4 cm, or 6 cm.  So the equation becomes:

 

108 = ∏(6²)h

 

So h = 108/(36∏)