Vessel, water and bar

Water is contained in the vessel of a rectangular prism to a certain height as shown in Fig.1.

The bar of a rectangular prism whose length and width at the bottom is 10 cm and 6 cm respectively was put into this vessel to 24 cm from the bottom of the vessel for the both bottom might be parallel.

In this case, the water surface was up to the place of the height 9/10 of the vessel.

Furthermore, when the bar is put in until it reach to the bottom of the vessel, 600 cm³ of water was overflowed.

Finally when the bar was taken out, the water surface came to 7/10 of the height of the vessel.

Answer

Answer the following questions.

(1) Find the ratio of the base area of the bar and the vessel.

(2) Find the depth of the vessel.

(3) Find the height of the water in the vessel first.