New Math Drill (Level 1) : Geometry(Solid figure) Problem3(1) NAKANO ATTACHED TO MEIJI UNV.-2014

There is a container whose all corners are the right angle as shown in the Fig.1 below. 

Water is put in 2/3 of the container. 

And the container is put on with the shaded face being placed in the bottom as shown in Fig.2. 

In this case, find the height of the water.

Answer

17/3 cm

Solution

The volume of the water is (6 × 8 - 3 × 2) × 3 × 2/3 = 84 cm³. 

The volume of A in Fig.3 is 3 × 6 × 3 = 54 cm³. 

The volume of B is 2 × 3 × 3 = 18 cm³. 

84 - (54 + 18) = 12 cm³ 

12 / (3 × 6) = 2/3 cm 

Therefore the height of the water is 3 + 2 + 2/3 = 17/3 cm